Question

Use the image below to answer the following question:12What relationship do the ratios of sin x° and cos yº share?12The ratios are both identical. ((andThe ratios are opposites. (andThe ratios are reciprocals. (and13The ratios are both negative. (12)and 2)

Answer 1

Given:

• Hypotenuse = 13

,

• Length of longer leg = 12

,

• Length of shorter leg = 5

Let's determine the relationship of the ratios of sin(x) and cos(y).

For sin(x), apply the trigonometric ratio formula for sine:

$sin\theta=\frac{\text{ opposite}}{\text{ hypotenuse}}$

Where:

θ is the angle = x

opposite side is the side opposite the angle = 12

Hypotenuse is the longest side of the triangle = 13

Thus, we have:

$sinx=\frac{12}{13}$

• For cos y:

Apply the trigonometric ratio formula for cosine:

$cos\theta=\frac{\text{ adjacent }}{hypotenuse}$

Where:

θ is the angle = y

Adjacent side is the side adjacent the angle = 12

Hypotenuse = 13

Thus, we have:

$\text{ cos}y=\frac{12}{13}$

Therefore, we can see that the ratios are the same:

$\begin{gathered} sinx=\frac{12}{13} \\ \\ cosy=\frac{12}{13} \end{gathered}$

ANSWER:

$\text{ The ratios are identical \lparen}\frac{12}{13}\text{ and }\frac{12}{13})$