Question

How do you solve cos((π/6)x)=0

Answer 1

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