Question

X=2π/3

Find the exact value of cos(x). Please include a drawing of your reference triangle to receive full credit.

Answer 1

`cos{(2\pi)/(3)}=-(1)/(2)`.

Reference angle is
`(\pi)/(3)`

Explanation:

Given the value of x. we have to find the correct value of cosx.

`x=(2\pi)/(3)`

Now, we have to find the exact value of
`cos{(2\pi)/(3)}`

`cos{(2\pi)/(3)}=cos((\pi)/(2)+(\pi)/(6))`

`=-sin((\pi)/(6))`

`=-(1)/(2)`

Now, we have to find the reference angle of
`x=(2\pi)/(3)`.

Since the angle
`x=(2\pi)/(3)` lies in second quadrant, the reference angle formula is

Reference angle=
`\pi-given angle`.

=
`\pi-(2\pi)/(3)=(\pi)/(3)`