Question

what relationship do the ratios of sin x° and cos y° share? the ratios are opposites. (4/5 and -4/5) the ratios are both negative. (-4/5 and -4/5) the ratios are both identical. (4/5 and 4/5) the ratios are reciprocals. (4/5 and 5/4)

Explanation:

Step1: Recall sine and cosine definitions

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$ and $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. For $\sin x^{\circ}$, the opposite side to angle $x$ is 4 and the hypotenuse is 5, so $\sin x^{\circ}=\frac{4}{5}$. For $\cos y^{\circ}$, the adjacent side to angle $y$ is 4 and the hypotenuse is 5, so $\cos y^{\circ}=\frac{4}{5}$.

Answer:

The ratios are both identical. ($\frac{4}{5}$ and $\frac{4}{5}$)