Question

What relationship do the ratios of sin x° and cos y° share?

Answer 1

Step-by-step explanation:

Step 1:  Find sin of x

$sin(x) = \frac{opposite}{hypotenuse}$

$sin(x)=\frac{12}{13}$

Step 2:  Find cos y

$cos(y)=\frac{adjacent}{hypotenuse}$

$cos(y)=\frac{12}{13}$

Step 3:  Find the relationship

Since sin(x) = 12/13 and cos(y) = 12/13, we can assume that sin(x) = cos(y)

Answer:  sin(x) = cos(y)

Answer 2

Answer:

sin(x) = cos(y)

Step-by-step explanation:

Let's figure out what sin(x) and cos(y) are before we figure out the relationship.

Sine is opposite / hypotenuse. Here, the opposite side to angle x is 12 and the hypotenuse is 13. So, sin(x) = 12/13.

Cosine is adjacent / hypotenuse. Here, the adjacent side of angle y is 12 and the hypotenuse is 13. So, cos(y) = 12/13.

Now we can see the relationship: sin(x) = cos(y)

In fact, for any right triangle with angles 90°, α°, and β°, where α and β can be any angle degree that add up to 90, the following relationships are true:

sin(α) = cos(β)

and

sin(β) = cos(α)