Question

If sin=3/5 then cos =

Answer 1

`\sin( \theta )=\cfrac{\stackrel{opposite}{3}}{\underset{hypotenuse}{5}} \hspace{5em}\textit{let's find the \underline{adjacent side}} \\\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=√(c^2 - o^2) \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{5}\\ a=adjacent\\ o=\stackrel{opposite}{3} \end{cases}`

`a=\pm√( 5^2 - 3^2)\implies a=\pm√( 25 - 9 ) \implies a=\pm√( 16 )\implies a=\pm 4 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill~\cos(\theta )=\pm\cfrac{\stackrel{adjacent}{4}}{\underset{hypotenuse}{5}} ~\hfill~`