Precalculus Inverse Trigonometric Functions and Equations Quiz: 10 Questions with Explanations

A \(\pi\)B 0C \(\frac{\pi}{2}\)D \(\frac{\pi}{4}\)

sin(pi/2) = 1, and pi/2 is in the range of arcsin.

A \(\left[-\frac{\pi}{2},\frac{\pi}{2}\right]\)B \([0,\pi]\)C \([-1,1]\)D \([0,2\pi]\)

Arccos returns angles from 0 to pi.

A \(\frac{\pi}{6}\)B \(\frac{\pi}{4}\)C \(\frac{\pi}{3}\)D \(\frac{2\pi}{3}\)

tan(pi/3) = sqrt3.

A \(y=\pm\pi\)B \(y=\pm1\)C \(y=0\)D \(y=\pm\frac{\pi}{2}\)

Arctan approaches pi/2 and -pi/2 as x goes to plus or minus infinity.

A \(\frac{5\pi}{6}\)B \(\frac{\pi}{6}\)C \(-\frac{\pi}{6}\)D \(\frac{\pi}{3}\)

sin(5pi/6) = 1/2, and arcsin(1/2) = pi/6 because it must be in the range.

A \(\frac45\)B \(\frac35\)C \(\frac54\)D \(\frac{3}{4}\)

A 3-4-5 triangle: the adjacent side is 4 and the hypotenuse 5.

A 1B 2C 3D 4

The line meets the curve at pi/6 and 5 pi/6.

A \(\frac{2\pi}{3},\frac{4\pi}{3}\)B \(\frac{\pi}{3},\frac{5\pi}{3}\)C \(\frac{\pi}{3},\frac{2\pi}{3}\)D \(\frac{4\pi}{3},\frac{5\pi}{3}\)

Cosine is negative in quadrants II and III with reference angle pi/3.

A \(\frac{\pi}{4}+2\pi k\)B \(\frac{\pi}{4}+\frac{\pi k}{2}\)C \(\pm\frac{\pi}{4}\)D \(\frac{\pi}{4}+\pi k\)

Tangent has period pi, so add pi k.

A \(\arcsin\frac{2}{10}\)B \(\arccos\frac{2}{10}\)C \(\arctan\frac{10}{2}\)D \(\sin\frac{2}{10}\)

The rise is opposite the angle and the ramp is the hypotenuse, so sin = 2/10.