Question

Sin theata=3/5, then cos theata= ?

Answer 1

`\bf sin(\theta )=\cfrac{\stackrel{opposite}{3}}{\stackrel{hypotenuse}{5}}\impliedby \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies √(c^2-b^2)=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ √(5^2-3^2)=a\implies \pm√(25-9)=a\implies \pm 4=a \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill cos(\theta )=\cfrac{\stackrel{adjacent}{\pm 4}}{\stackrel{hypotenuse}{5}}~\hfill`