Hello!
I have to solve this
tan 3θ = 0
what is then θ
there should be three values...
but my range is between -pi to +pi
Hello, domenfrandolic!
There are five solutions.
$\displaystyle \text{Solve: }\;\tan 3\theta \:=\: 0\quad\text{ for }\text{-}\pi < \theta < +\pi$
We have: .$\displaystyle \tan3\theta \:=\:0$
Then: .$\displaystyle 3\theta \:=\:\hdots\;\text{-}4\pi,\;\text{-}3\pi,\;\text{-}2\pi,\;\text{-}\pi,\;0,\;\pi,\;2\pi,\;3\pi,\;4\pi\;\hdots$
Hence: .$\displaystyle \theta \;=\;\hdots\;\text{-}\tfrac{4\pi}{3},\;\text{-}\pi,\;\text{-}\tfrac{2\pi}{3},\;\text{-}\tfrac{\pi}{3},\;0,\;\tfrac{\pi}{3},\;\tfrac{2\pi }{3},\;\pi,\;\tfrac{4\pi}{3}\;\hdots$
Therefore: .$\displaystyle \theta \;=\;\left\{\text{-}\frac{2\pi}{3},\;\text{-}\frac{\pi}{3},\;0,\;\frac{\pi}{3},\;\frac{2\pi}{3 }\right\}$