Question

Where are the x-intercepts for f(x) = −4cos(x − pi over 2) from x = 0 to x = 2π?

Answer 1

recall that to get the x-intercepts, we set the f(x) = y = 0, thus


`\bf \stackrel{f(x)}{0}=-4cos\left(x-(\pi )/(2) \right)\implies 0=cos\left(x-(\pi )/(2) \right) \\\\\\ cos^(-1)(0)=cos^(-1)\left[ cos\left(x-(\pi )/(2) \right) \right]\implies cos^(-1)(0)=x-\cfrac{\pi }{2} \\\\\\ x-\cfrac{\pi }{2}= \begin{cases} (\pi )/(2)\\\\ (3\pi )/(2) \end{cases}`


`\bf -------------------------------\\\\ x-\cfrac{\pi }{2}=\cfrac{\pi }{2}\implies x=\cfrac{\pi }{2}+\cfrac{\pi }{2}\implies x=\cfrac{2\pi }{2}\implies \boxed{x=\pi }\\\\ -------------------------------\\\\ x-\cfrac{\pi }{2}=\cfrac{3\pi }{2}\implies x=\cfrac{3\pi }{2}+\cfrac{\pi }{2}\implies x=\cfrac{4\pi }{2}\implies \boxed{x=2\pi }`