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?

Explanation:

Step1: Find the hypotenuse

By the Pythagorean theorem $c=\sqrt{a^{2}+b^{2}}$, where $a = 3$ and $b = 4$. So $c=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}=5$.

Step2: Calculate $\sin x^{\circ}$

The definition of sine in a right - triangle is $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. For $\sin x^{\circ}$, the opposite side to angle $x^{\circ}$ is $3$ and the hypotenuse is $5$. So $\sin x^{\circ}=\frac{3}{5}$.

Step3: Calculate $\cos y^{\circ}$

The definition of cosine in a right - triangle is $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. For $\cos y^{\circ}$, the adjacent side to angle $y^{\circ}$ is $3$ and the hypotenuse is $5$. So $\cos y^{\circ}=\frac{3}{5}$.

Step4: Determine the relationship

Since $\sin x^{\circ}=\frac{3}{5}$ and $\cos y^{\circ}=\frac{3}{5}$, we can say that $\sin x^{\circ}=\cos y^{\circ}$.

Answer:

$\sin x^{\circ}=\frac{3}{5}$, $\cos y^{\circ}=\frac{3}{5}$, and $\sin x^{\circ}=\cos y^{\circ}$