Chapter 6, Problem 39RE

To determine

Value of given trigonometric expression

Answer to Problem 39RE

  $\csc \frac{8\pi }{3}=\frac{2}{\sqrt{3}}$

Explanation of Solution

Given information:

  $\csc \frac{8\pi }{3}$

Formula used:

  $\csc \left(2n\left(\pi \right)+\theta \right)=\csc \left(\theta \right)$

  $\begin{array}{l}\csc \frac{8\pi }{3}\\ =\csc \left(\frac{6\pi +2\pi }{3}\right)\\ =\csc \left(2\pi +\frac{2\pi }{3}\right)\end{array}$

As,

  $\begin{array}{l}\csc \left(2n\left(\pi \right)+\theta \right)=\csc \left(\theta \right)\\ \csc \left(2\pi +\frac{2\pi }{3}\right)=\csc \frac{2\pi }{3}\end{array}$

  $\boxed{\csc \frac{8\pi }{3}=\csc \frac{2\pi }{3}=\frac{2}{\sqrt{3}}}$