# Math Help - trigonometry equation

1. ## trigonometry equation

How do I solve this? What is the answer?

tan3x=1, -pi/2<x<pi (this is the range that was given)

2. Hello, jcfulton!

Solve: . $\tan3x\:=\:1 \qquad -\frac{\pi}{2} \,< \,x\,<\,\pi$

We know that: . $\tan\tfrac{\pi}{4} \,=\,1$ . . . and there are other angles, right?

We have: . $\tan3x \:=\:1$

Hence: . $3x \;=\;\text{-}\frac{3\pi}{4},\:\frac{\pi}{4},\;\frac{5\pi}{4},\ :\frac{9\pi}{4}$

Therefore: . $x \;=\;\text{-}\frac{\pi}{4},\:\frac{\pi}{12},\:\frac{5\pi}{12}, \:\frac{3\pi}{4}$