Question

cosx=-1/2

Answer 1

45

Answer 2

-.- im actually glad now you left on my previous question because i want help not a stupid answer

Answer 3

cos(45)=sqrt(2)/2....

Answer 4

Have you heard of something called the unit circle?

Answer 5

Use a unit circle to find the value of x

you are looking for an angle that corresponds to a point (x,y) such that the x coordinate is equal to -1/2

Answer 6

here is a unit circle if you don't have one

http://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/720px-Unit_circle_angles_color.svg.png

Answer 7

thats what i was just looking up :D wait wouldnt it be 90 degrees?... that one seems to be more 1/2 than 45degrees does

Answer 8

it's not 90

cos(90) = 0 because the x coordinate of the point at 90 degrees is x = 0

Answer 9

which point has an x coordinate of -1/2 ?

Answer 10

well if were looking for x=1/2 then wouldnt it be 300 degrees?

Answer 11

not positive 1/2

negative 1/2

Answer 12

oh yeah c: okay so the angles would be 120 and 240

Answer 13

good, that means cos(120) = -1/2 and cos(240) = -1/2

Answer 14

those are just 2 of infinitely many angles because there are coterminal angles as well

Answer 15

yeah c:

Answer 16

so what we do to include all of them is add on 360*n where n is an integer

x = 120+360n or x = 240 + 360n

that includes all of the possible x values that make cos(x) = -1/2 true

Answer 17

but we can limit it down to degree 120 cuz 2 of my answers have 2pi/3 at the beginning c:

Answer 18

oh the answers are in radians, i see

Answer 19

yeah since 120 degrees = 2pi/3 radians, that means 2pi/3 is part of your answer

Answer 20

okay no...
these are my choices
cos x = -one divided by two

two pi divided by three plus n pi such that n equals zero, plus or minus one, plus or minus two to infinity

five pi divided by six plus n pi such that n equals zero, plus or minus one, plus or minus two to infinity

five pi divided by six plus two n pi comma seven pi divided by six plus two n pi such that n equals zero, plus or minus one, plus or minus two to infinity

two pi divided by three plus two n pi comma four pi divided by three plus two n pi such that n equals zero, plus or minus one, plus or minus two to infinity

Answer 21

woah .-. i ment for those to be numbers

Answer 22

if cos(theta) = -1/2

then which values of theta (in radians) make that equation true?

Answer 23

well yeah its 2pi/3 so that means 1st of 4th answer but i dont get the back part.... here

Answer 24

what the heck is going on at the end of that? .-.

Answer 25

the 4pi/3 comes from the angle 240 (240 degrees = 4pi/3 radians)

Answer 26

they are adding on 2pi*n to cover all of the coterminal angles (remember that 360 degrees = 2pi radians)

Answer 27

so the entire solution set can be generated by these equations

\[\Large x = \frac{2\pi}{3} + 2\pi n\]
\[\Large x = \frac{4\pi}{3} + 2\pi n\]

where n is an integer

Answer 28

no 360 degrees= 0 .-.

Answer 29

the rest of the stuff that says n = 0, +-1, +-2, etc just means "n is any integer"

Answer 30

well the answers are in radians, not degrees

Answer 31

oh they wrote it as 2npi not 2pi*n

but same idea

Answer 32

.-. where are you getting 2npi from?

Answer 33

2pi radians is equal to 360 degrees

Answer 34

that 2npi or 2pi*n is added on to make sure that you've included all of the coterminal angles

(it's the same idea as adding on 360n, just in radian mode)

Answer 35

okay thank you c:

Answer 36

you're welcome