Question

select the correct answer from each drop-down menu.
cos(420°) =
sin(450°) =

Explanation:

Step1: Simplify \( \cos(420^\circ) \)

Use the periodicity of cosine: \( \cos(\theta + 360^\circ n)=\cos\theta \) for integer \( n \).
\( 420^\circ = 360^\circ + 60^\circ \), so \( \cos(420^\circ)=\cos(360^\circ + 60^\circ)=\cos(60^\circ) \).
\( \cos(60^\circ)=\frac{1}{2} \).

Step2: Simplify \( \sin(450^\circ) \)

Use the periodicity of sine: \( \sin(\theta + 360^\circ n)=\sin\theta \) for integer \( n \).
\( 450^\circ = 360^\circ + 90^\circ \), so \( \sin(450^\circ)=\sin(360^\circ + 90^\circ)=\sin(90^\circ) \).
\( \sin(90^\circ)=1 \).

Answer:

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