Question

use the diagram to answer the question. which equation describes the relationship between sin x and cos y? sin x = cos y sin x = - cos y sin x = 90° - cos y sin x = 90° + cos y

Explanation:

Step1: Recall angle - sum property of a right - triangle

In a right - triangle, the sum of the two non - right angles is 90 degrees. So, for the given right - triangle with non - right angles \(x\) and \(y\), we have \(x + y=90^{\circ}\), which implies \(y = 90^{\circ}-x\).

Step2: Use the cosine formula

We know that \(\cos y=\cos(90^{\circ}-x)\). According to the co - function identity, \(\cos(90^{\circ}-\alpha)=\sin\alpha\) for any angle \(\alpha\). Substituting \(\alpha = x\) into the co - function identity, we get \(\cos(90^{\circ}-x)=\sin x\). Since \(y = 90^{\circ}-x\), then \(\cos y=\sin x\).

Answer:

\(\sin x=\cos y\)