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?

Answers:

sin(x) = 3/5

cos(y) = 3/5

They are both equal to the same value

Explanation:

Use the Pythagorean theorem to find the hypotenuse

a^2+b^2 = c^2

8^2+6^2 = c^2

100 = c^2

c^2 = 100

c = sqrt(100)

c = 10

The hypotenuse is 10 units long.

Now compute the sine of angle x.

sin(angle) = oppposite/hypotenuse

sin(x) = 6/10

sin(x) = 3/5

Also, find the cosine of angle y

cos(angle) = adjacent/hypotenuse

cos(y) = 6/10

cos(y) = 3/5

It turns out that sin(x) = cos(y) if and only if x+y = 90.