Chapter 5, Problem 29RE

To determine

Solve the given trigonometric function

Answer to Problem 29RE

The general form of solution.

  $x=\frac{\pi }{6}+n\pi$

Where $n$ is an integer.

Explanation of Solution

Given:

The trigonometric function.,

  $3\sqrt{3}\tan u=3$

By rewriting the trigonometric equation and isolating the trigonometric part on the left hand side.

  $\begin{array}{l}3\sqrt{3}\tan u=3\hfill \\ \tan u=\frac{3}{3\sqrt{3}}\hfill \\ \tan u=\frac{1}{\sqrt{3}}\hfill \end{array}$

Because $\tan x$ has a period of p, so find the solution in $\left[0,\pi \right)$

This solution is $x=\frac{\pi }{6}$

Finally add multiples of p to the obtained solution in $\left[0,\pi \right)$ to obtain a general form of solution.

  $x=\frac{\pi }{6}+n\pi$

Where $n$ is an integer.