Question

If sin(x) = cos(y) for acute angles x and y, how are the angles related?

a. congruent
b. complementary
c. supplementary
d. not enough information

Answer 1

b. complementary

Explanation:

-Complementary angles are angles that add up to 90°.

-These are usually the two acute angles in the right triangle.

#To verify, lets take the two angles 30° and 60°:

`Cos \ 60\textdegree=0.5\\\\Sin \ 30\textdegree=0.5\\\\\therefore Sin \ 30\textdegree=Cos \ 60 \textdegree=0.5`

#We can reverse as:

`Sin \ 60\textdegree=0.86603\\\\Cos \ 30\textdegree=0.86603\\\\\therefore Sin \ 60\textdegree=Cos \ 30\textdegree=0.86603`

Hence, two angles are said to be complimentary if they sum up to 90°.