Question

X=2π/3

Answer 1

Answer:

$cos{\frac{2\pi}{3}}=-\frac{1}{2}$.

Reference angle is $\frac{\pi}{3}$

Step-by-step explanation:

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

$x=\frac{2\pi}{3}$

Now, we have to find the exact value of $cos{\frac{2\pi}{3}}$

$cos{\frac{2\pi}{3}}=cos(\frac{\pi}{2}+\frac{\pi}{6})$

                $=-sin(\frac{\pi}{6})$

                 $=-\frac{1}{2}$

Now, we have to find the reference angle of $x=\frac{2\pi}{3}$.

Since the angle $x=\frac{2\pi}{3}$ lies in second quadrant, the reference angle formula is

Reference angle= $\pi-given angle$.

                           =$\pi-\frac{2\pi}{3}=\frac{\pi}{3}$