Exercises: Sine and Cosine of Complementary Angles

Two angles are complementary. One angle measures 35°. What is the measure of the other angle?

In a right triangle with acute angles $\alpha$ and $\beta$, which statement must be true?

In a right triangle with legs of length 3 and 4 and hypotenuse of length 5, if $\theta$ is the angle opposite the side of length 3, then $\sin(\theta) = \dfrac{\text{opposite}}{\text{hypotenuse}} = \dfrac{\hspace{0.2em}\fbox{\phantom{000000}}\hspace{0.2em}}{\hspace{0.2em}\fbox{\phantom{000000}}\hspace{0.2em}}$ and $\cos(\theta) = \dfrac{\text{adjacent}}{\text{hypotenuse}} = \dfrac{\hspace{0.2em}\fbox{\phantom{000000}}\hspace{0.2em}}{\hspace{0.2em}\fbox{\phantom{000000}}\hspace{0.2em}}$.

In right triangle $ABC$ with right angle at $C$, if $\angle A = 47\degree$, then $\angle B = \underline{\hspace{5em}}\degree$. The two acute angles are   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   angles.

Which equation correctly states the complementary angle relationship for sine and cosine?

Given that $\sin(32\degree) \approx 0.53$, use the complementary angle relationship to find $\cos(58\degree)$ without a calculator. $\cos(58\degree) = \sin(\underline{\hspace{5em}}\degree) \approx \underline{\hspace{5em}}$.

Given that $\cos(71\degree) \approx 0.326$, find $\sin(19\degree)$ without a calculator. $\sin(19\degree) = \cos(\underline{\hspace{5em}}\degree) \approx \underline{\hspace{5em}}$.

Simplify $\cos(90\degree - x)$. Your answer should be a single trig function of $x$: $\cos(90\degree - x) = \underline{\hspace{5em}}$.