Quiz about 12.1 Inverse Trigonometric Values

Question 1

In Quadrant I, what is the angle for which the tangent value is 1 and the sine and cosine values are equal?

Accepted Answer

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

Answer

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

Answer

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

Question 2

To have an inverse function, the domain of $$y=\sin x$$ is restricted to

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 3

To have an inverse function, the domain of $$y=\cos x$$ is restricted to

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 4

To have an inverse function, the domain of $$y= an x$$ is restricted to

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 5

Evaluate: $$\sin^{-1}\left(-\frac{\sqrt{3}}{2}\right)$$

Accepted Answer

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

Answer

$$-\frac{\pi}{2}$$

Answer

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

Answer

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

Answer

$$0$$

Question 6

Evaluate: $$ an ext{}^{-1}\left(-\frac{\sqrt{3}}{3} ight)$$

Accepted Answer

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

Answer

$$-\frac{\pi}{2}$$

Answer

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

Answer

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

Answer

$$0$$

Question 7

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

Accepted Answer

$$\frac{2\pi}{3}$$

Answer

$$\frac{\pi}{2}$$

Answer

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

Answer

$$\frac{5\pi}{6}$$

Answer

$$\pi$$

Question 8

Evaluate: $$\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)$$

Accepted Answer

$$\frac{5\pi}{6}$$

Answer

$$\frac{\pi}{2}$$

Answer

$$\frac{2\pi}{3}$$

Answer

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

Answer

$$\pi$$

Question 9

Which of the following has the greatest value?

Accepted Answer

$$\cos^{-1}\left(-1\right)$$

Answer

$$\sin^{-1}\left(-1\right)$$

Answer

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

Question 10

Which of the following is equal to $$ an^{-1}\left(-\sqrt{3} ight)$$ ?

Accepted Answer

$$\sin^{-1}\left(-\frac{\sqrt{3}}{2}\right)$$

Answer

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

Answer

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

Answer

$$\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)$$

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