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 the definition of sine

Sine of an angle in a right - triangle is $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. For $\sin x^{\circ}$, the side opposite to $x^{\circ}$ is $4$ and the hypotenuse is $5$. So, $\sin x^{\circ}=\frac{4}{5}$.

Step2: Recall the definition of cosine

Cosine of an angle in a right - triangle is $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. For $\cos y^{\circ}$, the side adjacent to $y^{\circ}$ is $4$ and the hypotenuse is $5$. So, $\cos y^{\circ}=\frac{4}{5}$.

Answer:

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