Chapter 4.2, Problem 46E

To determine

To evaluate the trigonometric function $\tan \left(\frac{5\pi }{7}\right)$ and round the answer to four decimal place using calculator .

Answer to Problem 46E

Using calculator, the value of $\tan \left(\frac{5\pi }{7}\right)$ is equivalent to $-1.2540$

Explanation of Solution

Given information :

Given trigonometric function $\tan \left(\frac{5\pi }{7}\right)$ .

Using calculator, the value of $\tan \left(\frac{5\pi }{7}\right)$ is equivalent to $-1.2540$ here the angle $\left(\frac{5\pi }{7}\right)$ is radian measure.

Since $\left(\frac{5\pi }{7}\right)$ is closure to $\frac{3\pi }{4}$ ,

  $\begin{array}{l}\Rightarrow \tan \left(\frac{5\pi }{7}\right)\simeq \tan \left(\frac{3\pi }{4}\right)\\ Thus,-1.254\simeq \tan \left(\frac{\pi }{2}+\frac{\pi }{4}\right)=-1\\ \therefore -1.254\simeq -1\end{array}$

Hence, the answer $\tan \left(\frac{5\pi }{7}\right)=-1.2540$ obtained by using calculator is correct.