Question

the measure of angle(theta) Is 2pi/3, which statements are true?

cos(theta) = √3/2

The measure of the reference angle is 30°.

The measure of the reference angle is 45°.

The measure of the reference angle is 60°.

tan(theta) = -√3

sin(theta)=-1/2​

Answer 1

Answer:

tan(theta) = -√3

sin(theta)=-1/2

Answer 2

Concept Introduction:-

Angles are the angles between $2$ bisecting lines or surfaces at or near their meeting point.

Given Information:-

We have been given that the measure of angle(theta) Is $2\pi /3$.

To Find:-

We have to find that the measure of angle(theta) Is $2\pi /3$, which statements are true

Solution:-

According to the problem

$cos (theta)=\sqrt{3/2}\\=cos30$

$theta=30$°

$tan$θ$=-\sqrt{3}=tan(90$°$+30$°$)$

$tan$θ$=tan120$°

θ$=120$°

$sin$θ$=-1/2$$=cos(90$°$+30$°$)$

$sin$θ$=sin120$°

θ$=120$°

Final Answer:-

The statement $cos(theta) =\sqrt{3/2}$ is true.