Answer:
[tex]cos{\frac{2\pi}{3}}=-\frac{1}{2}[/tex].
Reference angle is [tex]\frac{\pi}{3}[/tex]
Step-by-step explanation:
Given the value of x. we have to find the correct value of cosx.
[tex]x=\frac{2\pi}{3}[/tex]
Now, we have to find the exact value of [tex]cos{\frac{2\pi}{3}}[/tex]
[tex]cos{\frac{2\pi}{3}}=cos(\frac{\pi}{2}+\frac{\pi}{6})[/tex]
[tex]=-sin(\frac{\pi}{6})[/tex]
[tex]=-\frac{1}{2}[/tex]
Now, we have to find the reference angle of [tex]x=\frac{2\pi}{3}[/tex].
Since the angle [tex]x=\frac{2\pi}{3}[/tex] lies in second quadrant, the reference angle formula is
Reference angle= [tex]\pi-given angle[/tex].
=[tex]\pi-\frac{2\pi}{3}=\frac{\pi}{3}[/tex]
