Question

Use the image below to answer the following question. What relationship do the ratios of sin x° and cos y° share?A right triangle is shown. The two angles that are not 90 degrees are marked x and y. The leg across from angle y measuring 4, another leg across from angle x measuring 3, and the hypotenuse measuring 5 The ratios are both identical (three fifths and three fifths). The ratios are opposites (negative three fifths and three fifths). The ratios are reciprocals (three fifths and five thirds). The ratios are both negative (negative five thirds and negative three fifths).

Answer 1

Remember the definition of the sine and the cosine of an angle in a right triangle:

$\begin{gathered} \cos (\theta)=\frac{\text{Side adjacent to }\theta}{\text{Hypotenuse}} \\ \\ \sin (\theta)=\frac{\text{Side opposite to }\theta}{\text{ Hypotenuse}} \end{gathered}$

In the given triangle, the length of the hypotenuse is 5.

The side opposite to xº has a length of 3, then:

$\sin (xº)=\frac{3}{5}$

The side adjacent to yº has a length of 3, then:

$\cos (yº)=\frac{3}{5}$

As we can see, both cos(yº) and sin(xº) have the same value: 3/5.

Therefore, the correct choice is option 1:

The ratios are both identical (3/5 and 3/5).