Question

Trigonometric Identities and Applications? help

Answer 1

`\bf h=-15cos\left( (2\pi )/(5)t \right)\qquad \boxed{h=8}\qquad 8=-15cos\left( (2\pi )/(5)t \right) \\\\\\ \cfrac{8}{-15}=cos\left( (2\pi )/(5)t \right)\implies cos^(-1)\left( (8)/(-15)\right)=cos^(-1)\left[ cos\left( (2\pi )/(5)t \right) \right] \\\\\\ cos^(-1)\left( (8)/(-15)\right)=\cfrac{2\pi }{5}t\implies \cfrac{5}{2\pi }\cdot cos^(-1)\left( (8)/(-15)\right)=t\\\\ -------------------------------`


`\bf cos^(-1)\left( (8)/(-15)\right)=\stackrel{radians}{\stackrel{II~quadrant}{\approx 2.13}~~,~~\stackrel{III~quadrant}{\approx 4.15}}\qquad \qquad t= \begin{cases} (5)/(2\pi )\cdot 2.13\\\\ (5)/(2\pi )\cdot 4.15 \end{cases}`