Question

Use trigonometric identities and algebraic methods, as necessary, to solve the following trigonometric equation. Please identify all possible solutions by including allanswers in 10, x) and indicating the remaining answers by using n to represent any integer. Round your answer to four decimal places, if necessary. If there is no solution,indicate "No Solution."2tan(x) + 2/3 = 0

Answer 1

SOLUTION

The given equation is:

$2\tan x+2\sqrt[]{3}=0$

rewrite the equation as follows:

$2\tan x=-2\sqrt[]{3}$

Divide both sides by 2

$\begin{gathered} \tan x=\frac{-2\sqrt[]{3}}{2} \\ \tan x=-\sqrt[]{3} \end{gathered}$

Hence the value of x is

$\begin{gathered} x=\tan ^{-1}(-\sqrt[]{3})^{}_{} \\ x=\frac{2\pi}{3}+\pi n \end{gathered}$

Therefore using the given interval, the value of x is

$x=120^{\circ}$