Question

Find the trignometric function of $\frac{5{\pi }^{}}{6}$.

Answer 1

Given that, the angle $\frac{5\pi }{6}$

We know that,

$\frac{5\pi }{6}$ is located in second quadrant, so,

Sin and cosec will be positive and tan, cot, sec and cosec will be negative.

Then,

$\sin \left(\frac{5\pi }{6}\right)=\sin (\pi -\frac{\pi }{6})=\sin \frac{\pi }{6}=\frac{1}{2}$

$\cos \left(\frac{5\pi }{6}\right)=\cos (\pi -\frac{\pi }{6})=-\cos \frac{\pi }{6}=-\frac{\sqrt{3}}{2}$

$\tan \left(\frac{5\pi }{6}\right)=\tan (\pi -\frac{\pi }{6})=-\tan \frac{\pi }{6}=-\frac{1}{\sqrt{3}}$

$\cot \left(\frac{5\pi }{6}\right)=\cot (\pi -\frac{\pi }{6})=-\cot \frac{\pi }{6}=-\sqrt{3}$

$\sec \left(\frac{5\pi }{6}\right)=sec(\pi -\frac{\pi }{6})=-\sec \frac{\pi }{6}=-\frac{2}{\sqrt{3}}$

$\csc \left(\frac{5\pi }{6}\right)=\csc (\pi -\frac{\pi }{6})=\csc \frac{\pi }{6}=2$

Hence, this is the answer.