# Find the exact value of \cos\frac{5\pi}{3}

Find the exact value of $\mathrm{cos}\frac{5\pi }{3}$
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peterpan7117i
This angle $\mathrm{cos}\frac{5\pi }{3}$ is in the 4th quadrant, where cos ratio has a positive value.
Related acute angle is $\left(2\pi -\frac{5\pi }{3}\right)=\frac{\pi }{3}$
Thus, $\mathrm{cos}\frac{5\pi }{3}=\mathrm{cos}\frac{\pi }{3}$
Now, use the Exact value triangle for this angle:
$⇒\mathrm{cos}\frac{5\pi }{3}=\mathrm{cos}\frac{\pi }{3}=\frac{1}{2}$

godsrvnt0706
$\mathrm{cos}\frac{5\pi }{3}=\frac{1}{2}$