How do I solve this? What is the answer?

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

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- Nov 3rd 2008, 02:21 PMjcfultontrigonometry equation
How do I solve this? What is the answer?

tan3x=1, -pi/2<x<pi (this is the range that was given) - Nov 3rd 2008, 03:29 PMSoroban
Hello, jcfulton!

Quote:

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