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= (opposite\ side)/(hypotenuse) =(a)/(c)`, and


`\displaystyle{ \cos \beta= (adjacent\ side)/(hypotenuse) =(a)/(c)`


Answer: they are equal.