Question

Use the image below to answer the following question. Find the value of sin x® and cos y. What relationship do the ratios of sin x® and cos yº share?

Answer 1

let me not bore you to death, but by using the pythagorean theorem to get the hypotenuse, we get

$\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c = \sqrt{a^2+b^2}\implies c =5 \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}$

therefore

$sin(x) = \cfrac{\stackrel{opposite}{3}}{\underset{hypotenuse}{5}}~\hspace{10em} cos(y) = \cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{5}}$

now check the picture below

in a right-triangle, the sine of one of the acute angles is the same as the cosine of the other acute angle.