Question

How do you solve cos((π/6)x)=0

Answer 1

$\bf cos\left( \frac{\pi }{6}x \right)=0\implies cos^{-1}\left[ cos\left( \frac{\pi }{6}x \right) \right]=cos^{-1}(0) \\\\\\ \cfrac{\pi x}{6}=cos^{-1}(0)\implies \cfrac{\pi x}{6}= \begin{cases} \frac{\pi }{2}\\\\ \frac{3\pi }{2} \end{cases}\\\\ -------------------------------$

$\bf \cfrac{\pi x}{6}=\cfrac{\pi }{2}\implies \pi x=\cfrac{6\pi }{2}\implies x=\cfrac{6\pi }{2\pi } \implies \measuredangle x=\stackrel{radians}{3}\\\\ -------------------------------\\\\ \cfrac{\pi x}{6}=\cfrac{3\pi }{2}\implies\pi x=\cfrac{18\pi }{2}\implies x=\cfrac{18\pi }{2\pi }\implies \measuredangle x=\stackrel{radians}{9}$