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likoan [24]
3 years ago
10

X=2π/3

Mathematics
1 answer:
Marina86 [1]3 years ago
3 0

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}

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