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 y° share?

A right triangle is shown with one leg measuring 4 and another leg measuring 3. The angle across from the leg measuring 3 is marked x degrees, and the angle across from the leg measuring 4 is marked y degrees.

Answer 1

this is a 3, 4, 5 triangle right?

the \(x^\circ\) is representing \(\beta\)

that means the opposite side of the triangle is the bottom leg.

\[ \sin x^\circ=\frac{opposite}{hypotenuse} \]
where
\[ opposite=3~~~;~~~hypotenuse=5 \]
thus,
\[\sin x^\circ=\frac{3}{5} \]


b) lets find the \(\cos y^\circ \)

\( y^\circ\) represents \(\alpha\) which means that the adjacent is the bottom leg.

\[ \cos y^\circ =\frac{adjacent}{hypotenuse}\]

where
\[ adjacent=3~~~;~~~hypotenuse=5 \]
thus,
\[\cos y^\circ=\frac{3}{5} \]

can you determine what relationship do the ratios of sin \( x6\circ\) and cos \(y^\circ\) share?