Precalculus Radians and the Unit Circle Quiz: 10 Questions with Explanations

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

90 times pi/180 = pi/2. Mixing up 90 and 180 gives pi.

A \(120^{\circ}\)B \(60^{\circ}\)C \(240^{\circ}\)D \(150^{\circ}\)

Multiply by 180/pi: (2/3)(180) = 120.

A \(2\pi\)B \(8\pi\)C \(4\pi\)D \(\pi\)

s = r theta = 4 times pi/2 = 2 pi.

A \(\frac{\sqrt3}{2}\)B \(\frac{\sqrt2}{2}\)C \(\frac12\)D \(1\)

The point on the unit circle at pi/3 is (1/2, sqrt3/2), so cosine is 1/2.

A IB IIC IVD III

200 is between 180 and 270, which is quadrant III.

A \(-\frac12\)B \(\frac12\)C \(\frac{\sqrt3}{2}\)D \(-\frac{\sqrt3}{2}\)

Reference angle pi/6 in quadrant II, where sine is positive: 1/2.

A \(\frac{5\pi}{4}\)B \(\frac{3\pi}{4}\)C \(-\frac{3\pi}{4}\)D \(\frac{9\pi}{4}\)

Add 2 pi: pi/4 + 8 pi/4 = 9 pi/4.

A \(1\)B \(\sqrt3\)C \(-1\)D \(-\sqrt3\)

Reference angle pi/4 gives |tan| = 1, and tangent is negative in quadrant II.

A \((1,0)\)B \((0,1)\)C \((0,-1)\)D \((-1,0)\)

At pi/2 the terminal side points straight up: (cos, sin) = (0, 1).

A \(6\pi\)B \(12\pi\)C \(2\pi\)D \(18\pi\)

A = 1/2 r^2 theta = 1/2 times 36 times pi/3 = 6 pi. Forgetting the 1/2 gives 12 pi.