Subtitles section
Repeat sentence
Subtitles mode
Full screen
Previous
Next
x 1.0
Playback speed
More

Arc length of petal of polar graph

Video vocabulary

chug

Copy vocabulary

US / tʃʌɡ /

UK / tʃʌɡ /

C1
  • verb
  • To move slowly making low sounds like steam trains

take

Copy vocabulary

US / teɪk /

UK / tek /

A1
  • noun
  • Filming of a single scene for TV or the movies
  • verb
  • To accept something that is offered
  • To use a method of traveling, e.g. a bus or train
  • To use a camera to make (a photo)
  • To pick up something and go away with it
  • To study a subject in school
  • To attempt to pass (an exam)
  • To require a certain amount of time, money, space

curve

Copy vocabulary

US / kə:v /

UK / kɚv /

A2
  • noun
  • Smooth rounded line that is not straight
  • verb
  • To make something bend into a rounded shape

beta

Copy vocabulary

US / 'bi:tə /

UK / 'beɪtə /

B2
  • noun
  • Test version of a product or software

comma

Copy vocabulary

US / ˈkɒmə /

UK / ˈkɑ:mə /

B2
  • noun
  • Mark showing a pause or list in a sentence

petal

Copy vocabulary

US / ˈpetl /

UK / ˈpɛtl /

B2
  • noun
  • Delicate colored part of a flower

length

Copy vocabulary

US / leŋθ /

UK / leŋθ /

A2
  • noun
  • Distance from one end of a pool to the other
  • Measurement of distance or of time

all

Copy vocabulary

US / ɔ:l /

UK / ɔl /

A1
  • adverb
  • Completely; totally
  • determiner
  • Being every one of something
  • pronoun
  • 100% of something; the complete amount

bit

Copy vocabulary

US / bɪt /

UK / bɪt /

A1
  • noun
  • Device put in a horse's mouth to control it
  • Small piece of something
  • verb
  • (E.g. of fish) to take bait and be caught

derivative

Copy vocabulary

US / dɪˈrɪvətɪv /

UK / dɪˈrɪvətɪv /

B1
  • adjecitve
  • Not from original ideas; from somewhere else

encourage

Copy vocabulary

US / ɪn'kʌrɪdʒ /

UK / ɛnˈkɚrɪdʒ, -ˈkʌr- /

A2
  • verb
  • To increase the chance of something happening
  • To make someone more determined or confident

rewrite

Copy vocabulary

US / ˌri:'raɪt /

UK / riˈraɪt /

A2
  • verb
  • To write again to improve, or correct errors

red

Copy vocabulary

US / red /

UK / rɛd /

A1
  • adjecitve
  • Being the color of blood

figure

Copy vocabulary

US / ˈfiɡə /

UK / ˈfɪɡjɚ /

A1
  • noun
  • Your body shape
  • Numbers in a calculation
  • Doll-like thing meant to represent a person
  • Picture or diagram giving information in a text
  • Person who is very important or famous
  • Shape of a person seen indistinctly or in outline
  • Amount that is expressed in numbers
  • verb
  • To appear in a game, play or event
  • To calculate how much something will cost
  • To understand after thinking; work out

way

Copy vocabulary

US / weɪ /

UK / we /

A1
  • adverb
  • Used to emphasize the amount of something
  • noun
  • Particular aspect of something being thought about
  • One of various choices that could be made
  • Particular existing condition or state
  • (Often long) distance or length of time
  • How something is done
  • Route to go to a place
  • Small street
  • Usual behavior, emotions or habits of someone

end

Copy vocabulary

US / end /

UK / ɛnd /

A1
  • noun
  • The point where a process or activity stops
  • A point that marks the limit of something; finish
  • Goal or desired result
  • The tip, edge or limit of something
  • verb
  • To be the last part of something

prime

Copy vocabulary

US / praɪm /

UK / praɪm /

A2
  • adjecitve
  • Concerning the highest in quality or value
  • Concerning the highest level of achievement
  • Most important, chief importance in value
  • verb
  • To get a person ready for; prepare someone
  • To coat with paint to prepare it for the main coat

have

Copy vocabulary

US / həv /

UK / hæv /

A1
  • verb
  • To drink, smoke, eat or use something
  • To experience the effects of something
  • To organize an event, or join in an activity
  • To own, possess, or hold something
  • To cause to happen or produce a particular effect

part

Copy vocabulary

US / pɑ:t /

UK / pɑ:rt /

A1
  • adjecitve
  • To some degree; half; not fully
  • noun
  • Division of a book
  • Ratio of something, e.g. 3 of gin, 1 of tonic
  • A line in a person's hair, made with a comb
  • Character an actor plays on stage, movie, or TV
  • Some, but not all of a specific thing
  • Role in causing something to happen
  • verb
  • To make a line in a person's hair, by using a comb
  • To move two things apart creating a space
  • To leave someone, or to break off a relationship

six

Copy vocabulary

US / sɪks /

UK / sɪks /

A1
  • number
  • 6

choice

Copy vocabulary

US / tʃɔɪs /

UK / tʃɔɪs /

A1
  • adjecitve
  • Of good quality or taste; desirable
  • noun
  • Decision between two or more possibilities

see

Copy vocabulary

US / si: /

UK / si /

A1
  • verb
  • To go on a date with someone
  • To predict whether something is, or will be true
  • To understand what someone says
  • To use your eyes to look at something
  • To visit a place often for sightseeing or pleasure
  • To visit or meet with someone
  • To find out by waiting or looking
  • To watch (a game, movie or TV show)

radical

Copy vocabulary

US / ˈrædɪkl /

UK / ˈrædɪkəl,'rædɪkḷ /

B1
  • adjecitve
  • Very new and different from what is traditional
  • Concerning something's most basic part or form
  • noun
  • Person who believes in extreme political change

could

Copy vocabulary

US / kəd /

UK / kʊd /

A1
  • other
  • Past form of 'can' to mean have ability
  • Used to ask for something politely, or to offer

enjoy

Copy vocabulary

US / ɪnˈdʒɔɪ /

UK / ɛnˈdʒɔɪ /

A1
  • verb
  • To take pleasure in something

know

Copy vocabulary

US / nəʊ /

UK / noʊ /

A1
  • verb
  • To be familiar with a person or place, thing
  • To feel sure or be convinced about something
  • To discover or be aware of something
  • To be able to distinguish
  • To have knowledge of things

sine

Copy vocabulary

US / saɪn /

UK / saɪn /

C1
  • noun
  • Angle's ratio of side opposite hypotenuse

away

Copy vocabulary

US / ə'weɪ /

UK / əˈwe /

A1
  • adjecitve
  • Not present
  • adverb
  • Disappear completely
  • Doing something with a lot of energy
  • Not here; far from here; in a different direction
  • To a different area, location

polar

Copy vocabulary

US / ˈpəʊlə(r) /

UK / ˈpolɚ /

B1
  • adjecitve
  • Concerning the areas near the North or South poles

with

Copy vocabulary

US / wɪð /

UK / wɪð, wɪθ /

A1
  • preposition
  • As an employee of a certain company
  • Against something or someone
  • By using something as a means
  • Due to; because of
  • Including
  • Possessing as a feature
  • Related to
  • (Of the manner/attitude by which you do something)
  • Used to express that people or things are together

apply

Copy vocabulary

US / ə'plaɪ /

UK / əˈplaɪ /

A1
  • verb
  • To spread a substance or liquid over a surface
  • To commit your time and effort to doing something
  • To make something useful in a certain situation
  • To be relevant for a situation
  • To ask formally for (job, permission etc.)

good

Copy vocabulary

US / ɡʊd /

UK / ɡʊd /

A1
  • adjecitve
  • Proper, appropriate or right
  • (Of an amount) enough; plenty
  • Excellent; high quality
  • Acting well or properly; of moral character
  • In a positive or happy emotional state
  • noun
  • Advantage or benefit

give

Copy vocabulary

US / ɡɪv /

UK / ɡɪv /

A1
  • noun
  • Degree of flexibility in something, a material
  • verb
  • To hand over or present something to someone
  • To cause someone to have or experience something

zero

Copy vocabulary

US / ˈzɪərəʊ /

UK / ˈzɪroʊ /

A1
  • noun
  • Temperature when water turns to ice
  • number
  • Number 0
  • verb
  • To set a scale or other device to show 0

same

Copy vocabulary

US / seɪm /

UK / sem /

A1
  • adjecitve
  • Being equal in quality and amount
  • Identical; not different
  • Not changing; constant

color

Copy vocabulary

US / 'kʌlə(r) /

UK / ˈkʌlɚ /

A1
  • noun
  • Quality of things you can see, e.g. red, blue
  • Pink or red in your face, e.g. after being ill
  • The shade of someone's skin e.g. black, or yellow
  • verb
  • To change or affect someone's opinion
  • To make something colorful using colored pencils

not

Copy vocabulary

US / nɒt /

UK / nɑt /

A1
  • adverb
  • Word indicating the negative
  • (Used to form the negative of verbs)

our

Copy vocabulary

US / 'aʊə(r) /

UK / aʊr /

A1
  • determiner
  • Belonging to us

want

Copy vocabulary

US / wɔnt /

UK / wɑnt, wɔnt /

A1
  • noun
  • Something you desire or wish for
  • State or condition of poverty
  • verb
  • To desire or wish for something; hope for a thing

video

Copy vocabulary

US / 'vɪdɪəʊ /

UK / ˈvɪdiˌo /

A2
  • adjecitve
  • Of a moving film, with sound
  • noun
  • Recording capturing action with sound
  • verb
  • To make a moving film of, with sound

can

Copy vocabulary

US / kæn /

UK / kən,kæn /

A1
  • noun
  • A metal container for storing food
  • other
  • Able to; have the skill to; have the time to
  • verb
  • To have permission to
  • To be possible to do
  • To preserve food by sealing it in a metal container

sense

Copy vocabulary

US / sens /

UK / sɛns /

A1
  • noun
  • Certain mental feeling or emotion
  • Normal or clear state of mind
  • Meaning of a particular word, phrase or text
  • verb
  • To perceive using sight, sound, taste touch etc.
  • To recognize the presence of something

round

Copy vocabulary

US / raʊnd /

UK / raʊnd /

A1
  • adjecitve
  • Being in the shape of a circle or ball
  • Consisting of curved and not straight lines
  • Somewhat fat or curved in physical appearance
  • Being a whole number, not a fraction, decimal
  • adverb
  • From beginning to end (e.g. of the year)
  • noun
  • One of the three-minute periods in boxing
  • Drinks bought by one person for a group
  • Series regular visits, routes, or stops at places
  • Single shot or bullet fired from a gun
  • An object with a circular shape
  • One stage in a series of games, e.g. football
  • One's turn in a game such as cards
  • preposition
  • Going around
  • verb
  • To cause or make a circular or curved shape
  • To go or pass around the bend or corner
  • To change from a fraction to nearest whole number

blue

Copy vocabulary

US / blu: /

UK / blu /

A1
  • adjecitve
  • Color of the clear sky
  • Feeling sad or down

pick

Copy vocabulary

US / pɪk /

UK / pɪk /

A1
  • noun
  • Sharp tool used for breaking the ground
  • Item selected from a group of choices
  • verb
  • To take fruit or vegetables from a plant or tree
  • To decide on a thing from various choices; select
  • To remove (flower, etc.) with your fingers

would

Copy vocabulary

US / wʊd /

UK / wʊd /

A1
  • other
  • Used to indicate something imagined
  • Used to ask or request something politely
  • Verb used to indicate possibility, request etc.
  • Used to indicate a preference
  • Used to indicate a reaction
  • Indicates something that occurred repeatedly
  • Used to indicate willingness or ability to do

angle

Copy vocabulary

US / ˈæŋgl /

UK / ˈæŋɡəl /

B1
  • noun
  • Place where two lines or surfaces meet

equal

Copy vocabulary

US / 'i:kwəl /

UK / ˈikwəl /

A1
  • adjecitve
  • Same in shape, size, or number
  • verb
  • To add up or be the same as

formula

Copy vocabulary

US / 'fɔ:mjələ /

UK / ˈfɔrmjələ /

A2
  • noun
  • A mathematical or scientific rule
  • Plan, rule or method for doing or making something

now

Copy vocabulary

US / naʊ /

UK / naʊ /

A1
  • adverb
  • At the present time or moment
  • Right away or in the next possible moment
  • Used to refer to something that just happened
  • Time between the present and a moment in the past
  • conjunction
  • Resulting from or because of something

four

Copy vocabulary

US / fɔ:(r) /

UK / fɔr, for /

A1
  • number
  • 4

here

Copy vocabulary

US / hɪə(r) /

UK / hɪr /

A1
  • adverb
  • In this place; at this location, position or time

tool

Copy vocabulary

US / tu:l /

UK / tul /

A2
  • noun
  • Device used to make things, e.g. a hammer
  • verb
  • To provide a workshop with the right equipment

guess

Copy vocabulary

US / ɡes /

UK / ɡɛs /

A1
  • noun
  • Answer given when you don't know if it is correct
  • verb
  • To give an answer without knowing if it is correct

intuitive

Copy vocabulary

US / ɪnˈtju:ɪtɪv /

UK / ɪnˈtuɪtɪv, -ˈtju- /

B2
  • adjecitve
  • Able to understand by feeling rather than fact

ourselves

Copy vocabulary

US / ɑ:ˈselvz /

UK / aʊrˈsɛlvz, ɑr- /

A2
  • pronoun
  • (Showing speaker is affected by their own action)

will

Copy vocabulary

US / wɪl /

UK / wɪl /

A1
  • noun
  • Desire or choice of someone
  • Document saying who gets your money when you die
  • Strong desire to do something; determination
  • Desire to do something; strong wish to do
  • other
  • Used with verbs to express the future
  • verb
  • To leave property to someone after your death
  • To use mental effort to make something happen
  • Am (is, are) likely to do
  • To influence someone to do something
  • To make something happen by strongly wanting it

code

Copy vocabulary

US / kəʊd /

UK / kod /

A2
  • noun
  • A password made of a set of letters or numbers
  • Set of rules for behavior
  • A secret language using secret symbols
  • Written part of a computer program
  • verb
  • To express information in a series of numbers
  • To write a secret message using secret symbols
  • To write programs using computer languages

plus

Copy vocabulary

US / plʌs /

UK / plʌs /

A2
  • noun
  • A benefit or advantage
  • preposition
  • In addition; add
  • In addition to; Indicates a number above
  • Having a value greater than zero

too

Copy vocabulary

US / tu: /

UK / tu /

A1
  • adverb
  • In addition, also; with emphasis
  • Say that something is more than you want

actually

Copy vocabulary

US / ˈæktʃuəli /

UK / ˈæktʃuəli /

A1
  • adverb
  • Used to add new (often different) information

integral

Copy vocabulary

US / ˈɪntɪgrəl /

UK / ˈɪntɪɡrəl, ɪnˈtɛɡrəl /

B1
  • adjecitve
  • Being an essential part of something; necessary

write

Copy vocabulary

US / raɪt /

UK / raɪt /

A1
  • verb
  • To compose letters and words on paper or a screen
  • To invent or create a computer program
  • To create a song or piece of music

use

Copy vocabulary

US / ju:s /

UK / ju:s /

A1
  • noun
  • Ability to employ something
  • Need to enable it to work
  • Permission to do something with something
  • Act of spending money
  • Operation of a machine for its function
  • verb
  • To have; to eat, drink, consume etc.
  • To need to operate or work
  • To operate a machine, e.g. a computer
  • To treat a person badly
  • To do something with, for a task or purpose

integrate

Copy vocabulary

US / ˈɪntɪgreɪt /

UK / ˈɪntɪˌɡret /

A2
  • verb
  • To combine together; make into one thing

point

Copy vocabulary

US / pɔɪnt /

UK / pɔɪnt /

A1
  • noun
  • An item to be discussed
  • Small spot or dot
  • Fact or detail
  • Feature of something
  • The size of the text on a page or screen
  • A certain time or stage in a process
  • Certain position in time or space
  • Idea or fact you try to convince people about
  • Measurement of scores in a game, sport
  • Sharp end of something, e.g. a pen or pin
  • verb
  • To face a certain direction, e.g. north
  • To indicate something with your finger to others

sure

Copy vocabulary

US / ʃʊə(r) /

UK / ʃʊr /

A1
  • adjecitve
  • Having no doubts about something
  • Have confidence in your own words or actions
  • Firmly established or held; being firm or stable
  • Being correct or true
  • adverb
  • What you say to agree willingly

nine

Copy vocabulary

US / naɪn /

UK / naɪn /

A1
  • number
  • 9

two

Copy vocabulary

US / tu: /

UK / tu /

A1
  • number
  • 2

from

Copy vocabulary

US / frəm /

UK / frʌm, frɑm,frəm /

A1
  • preposition
  • Starting at a particular place, time or level

form

Copy vocabulary

US / fɔ:m /

UK / fɔrm /

A1
  • noun
  • Sports team or person's current winning record
  • Document you complete when making an application
  • Visible shape or style; type; kind
  • verb
  • To organize something such as a club or group
  • To develop; to come into a shape or substance
  • To make something into a particular shape

out

Copy vocabulary

US / aʊt /

UK / aʊt /

A1
  • adverb
  • No longer stylish (e.g. fashion)
  • Away from home, business, or the usual place
  • In a direction/movement away from inside or center
  • noun
  • Act when a batter cannot continue playing
  • verb
  • To tell people a secret

over

Copy vocabulary

US / 'əʊvə(r) /

UK / ˈovɚ /

A1
  • adverb
  • Finished; no longer happening
  • Towards the ground/away from a standing position
  • noun
  • A set of six consecutive balls bowled in cricket
  • other
  • Finished
  • preposition
  • Showing the relation when a thing is above another
  • On or covering something
  • Above or across something
  • More than you need
  • From one side to the other
  • In the direction of; toward

hey

Copy vocabulary

US / heɪ /

UK / he /

A1
  • exclamation
  • What you say when you want someone's attention

insert

Copy vocabulary

US / ɪnˈsɜ:t /

UK / ɪnˈsɜ:rt /

B1
  • noun
  • Act of putting into a certain place or spot
  • verb
  • To put something into a certain place or spot

real

Copy vocabulary

US / rɪəl /

UK / ˈriəl, ril /

A1
  • adjecitve
  • Actually existing or happening, not imagined
  • Being important or special

call

Copy vocabulary

US / kɔ:l /

UK / kɔl /

A1
  • noun
  • A order or request for action
  • The sound an animal makes, often when in danger
  • A correct prediction, e.g. a decision in a game
  • A short visit to a place or person
  • A decision by a referee or umpire in a game
  • verb
  • To make a request or order for action
  • (Animal) to make sounds to warn of danger
  • To announce the date of an election
  • To make a judgment about something
  • To give someone or something a name
  • To guess in advance the result or outcome
  • To visit a place or person for a short time
  • To phone someone
  • To speak, announce or shout in a loud voice

approximately

Copy vocabulary

US / əˈprɒksɪmətli /

UK / əˈprɑksəmɪtlɪ /

A2
  • adverb
  • Around; nearly; almost; about (a number)

far

Copy vocabulary

US / fɑ:(r) /

UK / fɑr /

A1
  • adjecitve
  • A long way away
  • Being a long way away
  • adverb
  • To a large degree or extent

theta

Copy vocabulary

US / ˈθi:tə /

UK / ˈθetə, ˈθi- /

C1
  • noun
  • 8th letter of the Greek alphabet

finding

Copy vocabulary

US / ˈfaɪndɪŋ /

UK / ˈfaɪndɪŋ /

A1
  • noun
  • Something you discover or find out; a result
  • verb
  • To become aware of something that is happening
  • To discover or meet by chance
  • To decide if someone is guilty of a crime, or not
  • To learn through study, research, or effort
  • To discover something by looking for it

come

Copy vocabulary

US / kʌm /

UK / kʌm /

A1
  • verb
  • To arrive at a place
  • (Of mail) to be delivered
  • To move toward someone; go with someone
  • To reach a certain point or state

help

Copy vocabulary

US / help /

UK / hɛlp /

A1
  • noun
  • Something given to enable a person to do something
  • Assistance given to someone in need
  • Someone who makes something easier or possible
  • verb
  • To act to enable a person to do something; assist
  • To make something better or less difficult

finally

Copy vocabulary

US / ˈfaɪnəli /

UK / ˈfaɪnəli /

A1
  • adverb
  • used especially at the beginning of a sentence to introduce the last point or idea
  • After a long time or some difficulty

variable

Copy vocabulary

US / ˈveəriəbl /

UK / ˈveriəbl /

A2
  • adjecitve
  • Having the ability to change or vary
  • noun
  • Mathematical quantity with several values

and

Copy vocabulary

US / ənd /

UK / ənd, ən,ænd /

A1
  • conjunction
  • Used to refer to two or more things
  • Plus; in addition; on top of that
  • Used to introduce an action that follows another

back

Copy vocabulary

US / bæk /

UK / bæk /

A1
  • adjecitve
  • Farthest from the front e.g. in a classroom
  • adverb
  • Have returned to a place you were before
  • noun
  • The part of a chair that the upper body leans upon
  • Location at the rear of something
  • The reverse of side something
  • Area on the rear of your body
  • verb
  • To bet money on something
  • To go backwards in a car
  • To support and encourage someone or some cause

estate

Copy vocabulary

US / ɪˈsteɪt /

UK / ɪˈstet /

A2
  • noun
  • A large piece of land, usually with a large house
  • Group of houses all built at the same time

hopefully

Copy vocabulary

US / ˈhəʊpfəli /

UK / ˈhopfəli /

A2
  • adverb
  • In a manner wishing something to happen

make

Copy vocabulary

US / meɪk /

UK / mek /

A1
  • noun
  • Product made by a particular company; brand
  • verb
  • To arrange or prepare something e.g. dinner
  • To get to (a place) on time
  • To gain the status of (teacher, lawyer, etc.)
  • To create something by putting things together
  • To earn a certain amount of money at a job
  • To cause or force a person to do something
  • To cause something to happen or be formed

this

Copy vocabulary

US / ðɪs /

UK / ðɪs /

A1
  • adjecitve
  • Used to indicate something already been discussed
  • Used to indicate something happening around now
  • adverb
  • An indication by a physical motion or gesture
  • A specific amount of
  • determiner
  • Person, thing, or idea near you
  • pronoun
  • Person, thing that has already been discussed

definite

Copy vocabulary

US / ˈdefɪnət /

UK / ˈdɛfənɪt /

A2
  • adjecitve
  • Not likely to change; clearly decided

alright

Copy vocabulary

US / ɔ:lˈraɪt /

UK / ɔlˈraɪt /

A2
  • adjecitve
  • OK; fine; good

one

Copy vocabulary

US / wʌn /

UK / wʌn /

A1
  • pronoun
  • You; we; people in general; someone
  • The thing or person previously referred to
  • adjecitve
  • Used to refer to people generally
  • Being a strong example of (something mentioned)
  • number
  • Number 1

root

Copy vocabulary

US / ru:t /

UK / rut, rʊt /

A2
  • noun
  • Emotional connection with a place, history etc.
  • The origin or starting place of something
  • A number that is multiplied by itself
  • Part of plant growing underground, as to get water
  • Part of tooth, hair etc. from which the rest grows
  • Base part of a word to which affixes can be added
  • verb
  • To cause a plant to develop or grow roots
  • (Animals) to search for e.g. food in earth
  • To stop someone moving, as through fear

little

Copy vocabulary

US / 'lɪtl /

UK / ˈlɪtl /

A1
  • adjecitve
  • Being short in length of time
  • Not great in size, amount, or degree; small
  • Being very young or younger than others
  • adverb
  • By an amount or degree that is not very much
  • Not often; rarely
  • noun
  • A person's name

let

Copy vocabulary

US / let /

UK / lɛt /

A1
  • verb
  • To allow someone to do something
  • Introducing a suggestion to do something together
  • To rent a house, etc. to others

the

Copy vocabulary

US / ðə /

UK / ðə /

A1
  • article
  • Used to refer to something already mentioned
  • Used to show there is only one of something
  • determiner
  • Used to describe all of a family

attempt

Copy vocabulary

US / ə'tempt /

UK / əˈtɛmpt /

A2
  • noun
  • Effort made to try to do or accomplish something
  • verb
  • To try to do something challenging or difficult

you

Copy vocabulary

US / jʊ /

UK / ju /

A1
  • pronoun
  • Person someone is speaking or writing to
  • Person or people in general

alpha

Copy vocabulary

US / ˈælfə /

UK / 'ælfə /

B1
  • adjecitve
  • Most powerful (animals of the same sex)
  • noun
  • First letter in the Greek alphabet

arc

Copy vocabulary

US / ɑ:k /

UK / ɑrk /

B2
  • noun
  • Smoothly curving line or movement
  • verb
  • To bend in a smooth curve

portion

Copy vocabulary

US / 'pɔ:ʃn /

UK / ˈpɔrʃən, ˈpor- /

B1
  • noun
  • Serving of food that is intended for one person
  • Part of something shared that belongs to a whole
  • verb
  • To separate something to divide among people

about

Copy vocabulary

US / ə'baʊt /

UK / əˈbaʊt /

A1
  • adverb
  • To be ready to; going to
  • Nearly; approximately; roughly
  • Near; next to; close to
  • In every direction; in the area of
  • preposition
  • Concerning or of (a topic)

care

Copy vocabulary

US / keə(r) /

UK / kɛr /

A1
  • noun
  • Treatment you receive for your health or safety
  • Something that a person worries about
  • verb
  • To feel interest, concern, or worry
  • To look after someone or something

second

Copy vocabulary

US / 'sekənd /

UK / ˈsɛkənd /

A1
  • adjecitve
  • 2nd; the one following first
  • noun
  • Unit of time; one sixtieth of a minute
  • Short period of time that you wait for someone
  • (Do) soon

that

Copy vocabulary

US / ðæt /

UK / ðæt, ðət /

A1
  • adjecitve
  • The person or thing being talked about
  • Used to identify something both the speakers know
  • adverb
  • Used to reinforce adjectives and adverbs
  • To such a degree
  • conjunction
  • Used to connect a noun clause
  • Used to introduce an adverbial clause
  • Used to introduce a noun clause
  • determiner
  • Used as a noun to refer to something
  • pronoun
  • Referring an object far away
  • Used to refer to the relative pronoun ‘which’

remind

Copy vocabulary

US / rɪ'maɪnd /

UK / rɪˈmaɪnd /

A2
  • verb
  • To cause someone to remember what they forgot

what

Copy vocabulary

US / wɒt /

UK / hwɑt, hwʌt, wɔt, wʌt,hwət, wət /

A1
  • pronoun
  • Thing or things that; the same kind as
  • Used to emphasize something you are about to say
  • adjecitve
  • Used to refer to a particular amount, or number
  • Used to place emphasis on a particular quality
  • adverb
  • To a certain degree
  • determiner
  • Question words used for asking for information
  • exclamation
  • Used to express excitement, shock, or surprise
  • Used to ask people to repeat something they said

analytically

Copy vocabulary

US / ˌænə'lɪtɪklɪ /

UK / ˌænə'lɪtɪklɪ /

B2
  • adverb
  • In an analytical manner; with detailed analysis

down

Copy vocabulary

US / daʊn /

UK / daʊn /

A1
  • adjecitve
  • Being sad, sick, or unhappy
  • Not operating, working, or functioning as expected
  • adverb
  • In a sitting or lying position
  • Towards or on the ground, floor, or bottom
  • Written or copied onto a piece of paper or book
  • noun
  • A period of play in American Football
  • The soft, smooth hairs that cover a bird's body
  • preposition
  • Along something's path, course, or direction
  • Going from a higher position to a lower position
  • verb
  • To eat or drink very quickly and without stopping

respect

Copy vocabulary

US / rɪ'spekt /

UK / rɪˈspɛkt /

A2
  • noun
  • Behavior that follows the established rules
  • Admiration for someone
  • Regard or admiration for someone or something
  • verb
  • To follow the established rules
  • To think very highly of another person

practice

Copy vocabulary

US / 'præktɪs /

UK / ˈpræktɪs /

A2
  • noun
  • The office and place for legal or medical work
  • Doing something many times to become better at it
  • verb
  • To work as a doctor or lawyer
  • To live according to the teachings of a religion
  • To do something many times to improve a skill

then

Copy vocabulary

US / ðen /

UK / ðɛn /

A1
  • adverb
  • A time that is not now
  • Following another thing in time or arrangement
  • Following on reasonably from what was just stated
  • At that time, not now

square

Copy vocabulary

US / skweə(r) /

UK / skwɛr /

A2
  • adjecitve
  • Being fair or honest
  • Multiply a number by itself e.g. 2x2 or 6x6
  • noun
  • Shape with 4 equal length sides and 4 equal angles
  • The result of multiplying Length by the width
  • Open public area in the middle of the town
  • verb
  • To make something balance or be equal
  • To multiply a number by itself, e.g. 2x2 or 6x8
  • To straighten the edge to form a four-sided shape

solve

Copy vocabulary

US / sɒlv /

UK / sɑ:lv /

A2
  • verb
  • To figure out a way to handle a difficult problem

everywhere

Copy vocabulary

US / ˈevriweə(r) /

UK / ˈevriwer /

A1
  • adverb
  • Every place

least

Copy vocabulary

US / li:st /

UK / list /

A1
  • adverb
  • In the smallest or lowest way
  • noun
  • Something that is of the lowest or smallest degree

right

Copy vocabulary

US / raɪt /

UK / raɪt /

A1
  • adjecitve
  • Correct or true
  • The south side of you looking at the rising sun
  • adverb
  • Exactly in a place or time
  • Being appropriate for a particular event
  • In a straight or direct manner
  • noun
  • Something you are legally or morally allowed to do
  • Ideal of what is just and good
  • Political view based on conservatism
  • verb
  • To fix something previously wrong or unjust
  • To make upright, as a boat that has turned over

get

Copy vocabulary

US / ɡet /

UK / ɡɛt /

A1
  • verb
  • To become affected by illness or disease
  • To begin to feel or understand an emotion or idea
  • To send or bring someone or something home, etc.
  • To go somewhere to obtain something
  • To (cause to) do a particular thing
  • To obtain, receive or be given something
  • To currently have
  • To prepare for use
  • To understand something being said or read

first

Copy vocabulary

US / fɜ:st /

UK / fɚst /

A1
  • adjecitve
  • 1st; Coming before all others in time or place
  • noun
  • Something that has not happened before
  • Position of the winner of a competition

case

Copy vocabulary

US / keɪs /

UK / kes /

A1
  • noun
  • Container used to carry things, e.g. clothes
  • Set of facts about a crime
  • Set of facts about an event
  • Example or instance of something
  • verb
  • To find out about a place, as in planning to steal

find

Copy vocabulary

US / faɪnd /

UK / faɪnd /

A1
  • noun
  • Object discovered by chance
  • Things that have been discovered from searching
  • verb
  • To become aware of something that is happening
  • To discover or meet by chance
  • To decide if someone is guilty of a crime, or not
  • To learn through study, research, or effort
  • To discover something by looking for it

type

Copy vocabulary

US / taɪp /

UK / taɪp /

A1
  • noun
  • Printed letters or blocks used for printing them
  • Group of things or people sharing common features
  • verb
  • To identify something belonging to a group
  • To write by touching keys on a keyboard

straightforward

Copy vocabulary

US / ˌstreɪtˈfɔ:wəd /

UK / stretˈfɔrwəd /

B1
  • adjecitve
  • Easy to do or understand; not complicated

phase

Copy vocabulary

US / feɪz /

UK / fez /

A2
  • noun
  • Different stages of the moon from new to full
  • Distinct part or step in a process
  • One stage of a process or series of stages
  • verb
  • To make happen in a gradual ordered way

myself

Copy vocabulary

US / maɪˈself /

UK / maɪˈsɛlf /

A1
  • pronoun
  • The same person who did the action mentioned
  • My regular, usual, or healthy self

for

Copy vocabulary

US / fə(r) /

UK / fɔr,fə /

A1
  • preposition
  • Used to show the purpose, or need of something

time

Copy vocabulary

US / taɪm /

UK / taɪm /

A1
  • noun
  • Speed at which music is played; tempo
  • Point as shown on a clock, e.g. 3 p.m
  • Number of hours, minutes needed to do something
  • Occasion when something happens
  • Period or occasion that something occurred
  • Period in history or the past
  • Something measured in minutes, hours, days, etc.
  • How long an event takes; duration
  • verb
  • To check speed at which music is performed
  • To choose a specific moment to do something
  • To measure how long an event takes, e.g. a race
  • To schedule something to occur at a specific moment

express

Copy vocabulary

US / ɪk'spres /

UK / ɪkˈsprɛs /

A1
  • adjecitve
  • Sent by a fast mail service
  • Traveling at high speed
  • noun
  • Fast train or bus
  • verb
  • To send something by fast mail
  • To state or show what you think or how you feel

pause

Copy vocabulary

US / pɔ:z /

UK / pɔz /

A2
  • noun
  • A temporary break before continuing
  • Function on a device to stop and restart it
  • Sign to hold a musical note a bit longer
  • verb
  • To stop doing for a while before continuing

multiplication

Copy vocabulary

US / ˌmʌltɪplɪˈkeɪʃn /

UK / ˌmʌltəplɪˈkeʃən /

B1
  • noun
  • Increase in the number of something
  • Process of multiplying one number by another

set

Copy vocabulary

US / set /

UK / sɛt /

A1
  • adjecitve
  • Prepared for something; ready
  • noun
  • Complete group of something
  • Place where a television show or movie is filmed
  • Group of games in a tennis match
  • Device that receives radio or television signals
  • verb
  • To make a clock state or ring at a particular time
  • To decide upon or choose something
  • To make something ready for use (e.g. table)
  • To decide on a price for something
  • To become hard (of glue, concrete etc.)
  • To be located in a specific place or time
  • To put (e.g. a vase) down carefully in a place
  • To put someone in a certain condition or state
  • (Of the sun) to go lower than the horizon

start

Copy vocabulary

US / stɑ:t /

UK / stɑrt /

A1
  • noun
  • First time or place that a thing exists; beginning
  • First opportunity to achieve something, e.g. a job
  • Sudden action or movement because you are scared
  • other
  • Beginning of something in place or time
  • verb
  • To do, be or happen for the first time; begin
  • To turn something on

graph

Copy vocabulary

US / græf /

UK / ɡræf /

A2
  • noun
  • Image expressing numerical data in lines or shapes
  • verb
  • To show data using images

just

Copy vocabulary

US / dʒʌst /

UK / dʒʌst /

A1
  • adjecitve
  • Proper or appropriate; as is deserved
  • Doing or being what is right or fair
  • Legally correct; having enough evidence
  • adverb
  • Almost; nearly
  • Exactly at the time of
  • Exactly (the same as, like)

eight

Copy vocabulary

US / eɪt /

UK / et /

A1
  • number
  • 8

interpret

Copy vocabulary

US / ɪn'tɜ:prɪt /

UK / ɪnˈtɚprɪt /

A2
  • verb
  • To express so that others understand it
  • To translate what is said into another language

calculator

Copy vocabulary

US / 'kælkjʊleɪtə(r) /

UK / ˈkælkjəˌletɚ /

B2
  • noun
  • A small electronic device used for calculation

replace

Copy vocabulary

US / rɪ'pleɪs /

UK / rɪˈples /

A2
  • verb
  • To use instead of something else
  • To return an item to its original location
  • Subtitles section
  • - What I want to do in this video is find the arc length of one petal, I guess we could call it, of the graph of r is equal to four sine of two theta.
  • So I want to find the length of this portion of the curve that is in red right over here.
  • We'll do this in two phases.
  • First of all I want to set up the definite integral for finding that arc length, and then we'll evaluate it.
  • I'll actually use a calculator to evaluate it because it'll be a little bit more straightforward at least for this integral.
  • Let's just start with that.
  • I encourage you to pause the video.
  • Knowing what we know about the formula for arc length, when we have it in polar form, see if you can apply it to figure out this arc length right over here.
  • I'm assuming you've had a go at it, so let's remind ourselves that the arc length is going to be the integral from our starting angle to our ending angle, we'll call it from alpha to beta, of the square root of the derivative of our function.
  • Which respect to theta squared, plus our function squared.
  • Plus our function squared d theta.
  • Let's figure out what r prime of theta and what r of theta actually are.
  • I'll color code it.
  • R prime of theta, we know what r of theta is let me just rewrite it.
  • We know r of theta is equal to four sine of two theta.
  • Our prime of theta is just going to be derivative of two theta with respect to theta is two times four is eight, derivative of sine is cosine, cosine of two theta.
  • If we wanted to write the definite integral for arc length it's going to be equal to the definite integral.
  • What's our starting bound?
  • For the petal that we care about, we're going to start at an angle of zero radians.
  • When we have an angle of zero radians, r is zero, that's this point right over here.
  • We're going to start at zero radians.
  • And we're going to go all the way up to pi over two.
  • When sine of two times pi over two is sine of pi, which is zero, so we'll get back to this point right over here.
  • We're going to go from zero to pi over two, to pi over two radians.
  • It's going to be the square root of, give myself some real estate here, r prime of theta squared is going to be this thing squared.
  • It's going to be 60-- Let me do it in that same blue color, it's going to be 64 cosine squared of two theta, then plus this squared which is going to be 16 sine squared of two theta, then of course we have our d theta.
  • You can attempt to solve this or evaluate this analytically, it's not too straightforward so I'm going to use a calculator.
  • It just gives us a practice with knowing that hey, there are tools out there that can help us do these types of things.
  • I'll go to the definite integral, I'll go to second calculus on my t 85, I picked this choice, which is for the definite integral.
  • Let me express when I'm taking the definite integral of, it's going to be the square root of 64 times cosine of two theta squared.
  • I'm going to use x instead of theta just because it's an easier variable to use on my calculator.
  • Cosine of two-- Actually let me make sure my parenthesis are good.
  • Cosine of two x, alright I'll close that.
  • Now I want to square that.
  • I did that first part.
  • Plus 16 times plus 16 times 16 times sine of two x.
  • Close that, close that.
  • Squared.
  • I'm not sure if the calculator knows to interpret that as multiplication, so let me insert a times right over here.
  • 64 times cosine of two x, that thing squared.
  • Plus 16 times sine of two x, that thing squared.
  • Let me go to the end.
  • Let me close my radical, so that's going to close that right over there, that closes what I'm taking the square root of.
  • Then comma, the variable that I'm integrating with respect to is x, in this case.
  • Everywhere I saw theta here I'm just replacing with an x there.
  • I want to do it from, instead of theta equals zero to theta equals pi over two, we'll say x is equal to zero to x is equal to pi over two.
  • Hopefully I have not made a mistake when I've typed this in, And I get...
  • It's chugging on a little bit.
  • And we get...
  • Will it actually come up?
  • Oh finally!
  • If we were to round it to the nearest thousandth it'll be nine point six eight eight.
  • Approximately nine point six eight eight.
  • Let's just see, does that make intuitive sense?
  • It goes as far as four away, so if you just went out to four and then back down that would be about eight.
  • Of course we have actually gone out some, so it actually makes intuitive sense that this arc length would be nine point six eight eight.
  • Hopefully you enjoyed that.