Question

What is the relationship between the sine and cosine of complementary angles in a right triangle? Please give an example to support your answer.

Answer 1

Consider the right triangle ABC with sides a, b, and c as shown in the figure. 

Let $m(\angle A)=\alpha$, and $m(\angle B)=\beta$.


$\alpha +\beta=90^{\circ}$, so angles A and B are complementary.


According to the definition of sine, and cosine:

$\displaystyle{ \sin \alpha= \frac{opposite\ side}{hypotenuse} =\frac{a}{c}$, and

$\displaystyle{ \cos \beta= \frac{adjacent\ side}{hypotenuse} =\frac{a}{c}$


Answer: they are equal.