Question

Decide if the two trigonometric functions areequal. Choose Yes or No.

Answer 1

Answer:

A. Yes

B. No

Explanation:

A. Recall the below rules;

$\begin{gathered} \cos(-x)=\cos x \\ \sin x=\cos(\frac{\pi}{2}-x) \end{gathered}$

We'll go ahead and apply the above rules to simplify the given trig. functions as seen below;

$\sin\frac{23\pi}{3}=\cos(\frac{\pi}{2}-\frac{23\pi}{3})=\cos(-\frac{43\pi}{6})=\cos(\frac{43\pi}{6})=\cos(\frac{7\pi}{6})=-\frac{\sqrt{3}}{2}$$\cos\frac{-17\pi}{6}=\cos\frac{17\pi}{6}=\cos\frac{5\pi}{6}=-\frac{\sqrt{3}}{2}$

We can see that both trig functions are equal so we'll choose Yes.

B.

Let's go ahead and simplify the given trig functions as seen below;

$\tan\frac{13\pi}{4}=\tan\frac{\pi}{4}=1$$\begin{gathered} Recall\text{ that }\tan(-x)=-\tan(x) \\ \tan\frac{-13\pi}{4}=-\tan\frac{13\pi}{4}=-\tan\frac{\pi}{4}=-1 \end{gathered}$

We can see that the two trig functions are not equal, so we'll choose No.