Algebra 2 Radians and the Unit Circle Quiz: 10 Questions with Explanations

A \(\pi\)B \(2\pi\)C \(\frac{\pi}{2}\)D \(180\pi\)

A half turn is π radians; a full turn is 2π.

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

90 · π/180 = π/2.

A 2.5 inchesB 7 inchesC 10π inchesD 10 inches

s = rθ = 5 · 2 = 10. The angle is already in radians, so no π is needed.

A \(\left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right)\)B \(\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right)\)C \(\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)\)D \(\left(1, \frac{\pi}{3}\right)\)

At 60 degrees the x-coordinate (cosine) is 1/2 and the y-coordinate (sine) is √3/2.

A -1B 0C 1D undefined

The point at π is (-1, 0), so cosine is the x-coordinate -1.

A \(\frac{1}{2}\)B \(-\frac{\sqrt{3}}{2}\)C \(\frac{\sqrt{3}}{2}\)D \(-\frac{1}{2}\)

The angle is in quadrant III with reference angle π/6, so sine is negative: -1/2.

A Quadrant IIIB Quadrant IC Quadrant IID Quadrant IV

In quadrant III, both sine and cosine are negative, so tangent (their ratio) is positive.

A 0B 1C √2/2D undefined

sin and cos are both √2/2, so their ratio is 1.

A \(\frac{7\pi}{6}\)B \(\frac{11\pi}{6}\)C \(\frac{\pi}{6}\)D \(\frac{2\pi}{3}\)

5π/6 and π/6 are mirror images across the y-axis, so they have the same y-coordinate (sine).

A \(\frac{4\pi}{3}\)B \(\frac{2\pi}{3}\)C \(\frac{7\pi}{3}\)D \(-\frac{\pi}{6}\)

Adding a full turn (2π) gives π/3 + 2π = 7π/3.