Chapter 13.2, Problem 9WE

To determine

To show: The sum of an even function and an odd function.

Answer to Problem 9WE

The sum of an even function and an odd function $\sin \frac{\pi }{3}=\frac{\sqrt{3}}{2}$

  $\cos \frac{\pi }{3}=\frac{1}{2}$

  $\tan \frac{\pi }{3}=\sqrt{3}$

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

  $\sec \frac{\pi }{3}=2$

  $\cot \frac{\pi }{3}=\frac{1}{\sqrt{3}}$.

Explanation of Solution

Calculation:

We know that $\frac{\pi }{3}$ radius $={60}^0$ .

$\theta$	$\sin \theta$	$\cos \theta$	$\tan \theta$	$\csc \theta$	$\sec \theta$	$\cot \theta$
${30}^0$	$\frac{1}{2}$	$\frac{\sqrt{3}}{2}$	$\frac{\sqrt{3}}{2}$	$2$	$\frac{2\sqrt{3}}{3}$	$\sqrt{3}$
${40}^0$	$\frac{\sqrt{2}}{2}$	$\frac{\sqrt{2}}{2}$	$1$	$\sqrt{2}$	$\sqrt{2}$	$1$
${60}^0$	$\frac{\sqrt{3}}{2}$	$\frac{1}{2}$	$\sqrt{3}$	$\frac{2\sqrt{3}}{3}$	$2$	$\frac{\sqrt{3}}{2}$

Therefore, From the table, we get the values of six trigonometric functions as follows:

  $\sin \frac{\pi }{3}=\frac{\sqrt{3}}{2}$

  $\cos \frac{\pi }{3}=\frac{1}{2}$

  $\tan \frac{\pi }{3}=\sqrt{3}$

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

  $\sec \frac{\pi }{3}=2$

  $\cot \frac{\pi }{3}=\frac{1}{\sqrt{3}}$