Question

the unit circle: mastery test
2
select the correct answer from each drop - down menu.
cos(420°)=
sin(450°)=

Explanation:

Step1: Reduce the angle for cosine

We know that the cosine function has a period of $360^{\circ}$. So, $\cos(420^{\circ})=\cos(360^{\circ} + 60^{\circ})$. According to the periodic - property of the cosine function $\cos(A + 360^{\circ})=\cos(A)$, then $\cos(360^{\circ}+60^{\circ})=\cos(60^{\circ})=\frac{1}{2}$.

Step2: Reduce the angle for sine

The sine function has a period of $360^{\circ}$. So, $\sin(450^{\circ})=\sin(360^{\circ}+90^{\circ})$. According to the periodic - property of the sine function $\sin(A + 360^{\circ})=\sin(A)$, then $\sin(360^{\circ}+90^{\circ})=\sin(90^{\circ}) = 1$.

Answer:

$\cos(420^{\circ})=\frac{1}{2}$, $\sin(450^{\circ}) = 1$