Quiz about Inverse Trig Functions: Restricted Domains

Question 1

What is the restricted domain of sine?

Accepted Answer

$$\left[-\frac{\Pi}{2},\frac{\Pi}{2}\right]$$

Answer

$$\left(-\frac{\Pi}{2},\frac{\Pi}{2}\right)$$

Answer

$$\left[0,\Pi\right]$$

Answer

$$\left(0,\Pi\right)$$

Question 2

What is the restricted domain of cosine?

Accepted Answer

$$\left[0,\Pi\right]$$

Answer

$$\left[-\frac{\Pi}{2},\frac{\Pi}{2}\right]$$

Answer

$$\left(-\frac{\Pi}{2},\frac{\Pi}{2}\right)$$

Answer

$$\left(0,\Pi\right)$$

Question 3

What is the restricted domain of tangent?

Accepted Answer

$$\left(-\frac{\Pi}{2},\frac{\Pi}{2}\right)$$

Answer

$$\left[-\frac{\Pi}{2},\frac{\Pi}{2}\right]$$

Answer

$$\left[0,\Pi\right]$$

Answer

$$\left(0,\Pi\right)$$

Question 4

Evaluate. $$\sin^{-1}\left(\frac{-\sqrt[]{2}}{2}\right)$$

Accepted Answer

$$\frac{-\pi}{4}$$

Answer

$$\frac{7\pi}{4}$$

Answer

$$\frac{\pi}{4}$$

Answer

$$\frac{3\pi}{4}$$

Question 5

Evaluate. $$\cos^{-1}\left(\frac{-\sqrt[]{2}}{2}\right)$$

Accepted Answer

$$\frac{3\pi}{4}$$

Answer

$$\frac{7\pi}{4}$$

Answer

$$\frac{-\pi}{4}$$

Answer

$$\frac{\pi}{4}$$

Question 6

Evaluate. $$ an^{-1}\left(1 ight)$$

Accepted Answer

$$\frac{\pi}{4}$$

Answer

$$\frac{7\pi}{4}$$

Answer

$$\frac{-\pi}{4}$$

Answer

$$\frac{3\pi}{4}$$

Question 7

Evaluate. $$\sin^{-1}\left(\frac{1}{2}\right)$$

Accepted Answer

$$\frac{\pi}{6}$$

Answer

$$\frac{\pi}{3}$$

Answer

$$\frac{-\pi}{6}$$

Answer

$$\frac{-\pi}{3}$$

Question 8

Evaluate. $$\cos^{-1}\left(\frac{1}{2}\right)$$

Accepted Answer

$$\frac{\pi}{3}$$

Answer

$$\frac{\pi}{6}$$

Answer

$$\frac{-\pi}{6}$$

Answer

$$\frac{-\pi}{3}$$

Question 9

Evaluate. $$ an^{-1}\left(-\sqrt[]{3} ight)$$

Accepted Answer

$$\frac{-\pi}{3}$$

Answer

$$\frac{\pi}{3}$$

Answer

$$\frac{\pi}{6}$$

Answer

$$\frac{-\pi}{6}$$

Question 10

Evaluate. $$ an^{-1}\left(-\frac{\sqrt[]{3}}{3} ight)$$

Accepted Answer

$$\frac{-\pi}{6}$$

Answer

$$\frac{\pi}{3}$$

Answer

$$\frac{\pi}{6}$$

Answer

$$\frac{-\pi}{3}$$

Inverse Trig Functions: Restricted Domains

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