How do I solve this? What is the answer?
tan3x=1, -pi/2<x<pi (this is the range that was given)
Hello, jcfulton!
Solve: .$\displaystyle \tan3x\:=\:1 \qquad -\frac{\pi}{2} \,< \,x\,<\,\pi$
We know that: .$\displaystyle \tan\tfrac{\pi}{4} \,=\,1$ . . . and there are other angles, right?
We have: .$\displaystyle \tan3x \:=\:1$
Hence: .$\displaystyle 3x \;=\;\text{-}\frac{3\pi}{4},\:\frac{\pi}{4},\;\frac{5\pi}{4},\ :\frac{9\pi}{4} $
Therefore: .$\displaystyle x \;=\;\text{-}\frac{\pi}{4},\:\frac{\pi}{12},\:\frac{5\pi}{12}, \:\frac{3\pi}{4}$