# What are the six trig function values of  (5pi)/3?

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Nghi N Share
May 17, 2018

Use trig table and unit circle -->
$\sin \left(\frac{5 \pi}{3}\right) = \sin \left(- \frac{\pi}{3} + \frac{6 \pi}{3}\right) = \sin \left(- \frac{\pi}{3}\right) = - \sin \frac{\pi}{3} = - \frac{\sqrt{3}}{2}$
$\cos \left(\frac{5 \pi}{3}\right) = \cos \left(- \frac{\pi}{3} + 2 \pi\right) = \cos \left(- \frac{\pi}{3}\right) = \cos \left(\frac{\pi}{3}\right) = \frac{1}{2}$
$\tan \left(\frac{5 \pi}{3}\right) = \frac{\sin}{\cos} = \left(\frac{\sqrt{3}}{2}\right) \left(\frac{2}{1}\right) = \sqrt{3}$
$\cot \left(\frac{5 \pi}{3}\right) = \frac{1}{\tan} = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}$
$\sec \left(\frac{5 \pi}{3}\right) = \frac{1}{\cos} = 2$
$\csc \left(\frac{5 \pi}{3}\right) = \frac{1}{\sin} = \frac{2}{\sqrt{3}} = 2 \frac{\sqrt{3}}{3}$

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