Module 7 Module Quiz Extension 1

Module 7 Quiz

15 multiple choice questions across the four lessons on inverse trigonometric functions: definitions and principal domains and ranges, graphs, exact values, key properties, and solving equations.

Module 7 Quiz

Q11 MARK

The principal range of $y = \sin^{-1} x$ is

A$[-\pi/2, \pi/2]$ B$[0, \pi]$ C$(-\pi, \pi]$ D$[0, 2\pi]$

Q21 MARK

The domain of $y = \cos^{-1} x$ is

A$x > 0$ Ball real numbers C$[0, \pi]$ D$[-1, 1]$

Q31 MARK

The principal range of $y = \tan^{-1} x$ is

A$[0, \pi]$ B$(-\pi/2, \pi/2)$ C$[-1, 1]$ D$[0, 2\pi]$

Q41 MARK

What is $\sin^{-1}(1/2)$?

A$5\pi/6$ B$-\pi/6$ C$\pi/6$ D$\pi/3$

Q51 MARK

What is $\cos^{-1}(-1/2)$?

A$4\pi/3$ B$\pi/3$ C$-\pi/3$ D$2\pi/3$

Q61 MARK

What is $\tan^{-1}(1)$?

A$\pi/2$ B$-\pi/4$ C$\pi/4$ D$3\pi/4$

Q71 MARK

The graph of $y = \sin^{-1} x$ is obtained by reflecting the restricted sine graph in

Athe x-axis Bthe line $y = x$ Cthe y-axis Dthe line $y = -x$

Q81 MARK

Which expression is defined for every real $x$?

A$\tan^{-1} x$ B$\sin^{-1} x$ C$\sqrt{1 - x^2}$ D$\cos^{-1} x$

Q91 MARK

If $\cos^{-1} x = \pi/3$, then $x$ equals

A$1$ B$-1/2$ C$\sqrt{3}/2$ D$1/2$

Q101 MARK

If $\sin^{-1} x = -\pi/6$, then $x$ equals

A$1/2$ B$-1/2$ C$-\sqrt{3}/2$ D$\sqrt{3}/2$

Q111 MARK

Which identity is valid for $-1 \le x \le 1$?

A$\cos^{-1}(\cos x) = x$ for all real $x$ B$\tan(\tan^{-1} x) = 1$ C$\sin(\sin^{-1} x) = x$ D$\sin^{-1} x = 1/\sin x$

Q121 MARK

For $0 \le x \le \pi$, $\cos^{-1}(\cos x)$ equals

A$x$ B$-x$ C$2\pi - x$ D$\pi - x$

Q131 MARK

The graph of $y = \tan^{-1} x$ has horizontal asymptotes

A$y = 0$ and $y = \pi$ B$y = -1$ and $y = 1$ C$x = -\pi/2$ and $x = \pi/2$ D$y = -\pi/2$ and $y = \pi/2$

Q141 MARK

The equation $\sin^{-1} x = \cos^{-1} x$ has solution

A$x = 0$ B$x = -1/\sqrt{2}$ C$x = 1/\sqrt{2}$ D$x = 1$

Q151 MARK

Which value is outside the range of $\cos^{-1} x$?

A$0$ B$\pi/2$ C$3\pi/2$ D$\pi$

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