Angles, Radians and the Unit Circle: Precalculus Math Test – PDF Download

Precalculus Unit Circle Test: questions 1–5

Question 1: Converting angle measures (2 points)

1. Convert \(225^{\circ}\) to radians. (1 point)
2. Convert \(\frac{7\pi}{6}\) to degrees. (1 point)

Question 2: Coterminal and reference angles (2 points)

1. Find the angle in \([0,2\pi)\) that is coterminal with \(\frac{23\pi}{6}\). (1 point)
2. Find the reference angle of \(\frac{23\pi}{6}\). (1 point)

Question 3: Point on the unit circle (3 points)

The figure shows the angle \(\theta=\frac{7\pi}{6}\) on the unit circle.

1. Write the exact coordinates of \(P\). (1 point)
2. Find \(\tan\frac{7\pi}{6}\). (1 point)
3. Find \(\sin(-\frac{7\pi}{6})\). (1 point)

Question 4: Arc length of a sector (2 points)

A pizza slice is a sector with radius 15 in.

1. Write the central angle in radians. (1 point)
2. Find the length of the curved crust, to two decimal places. (1 point)

Question 5: Angular and linear speed (3 points)

A Ferris wheel of radius 50 ft makes one full revolution every 8 minutes.

1. Find its angular speed in radians per minute. (1 point)
2. Find the linear speed of a rider in feet per minute, to two decimal places. (1 point)
3. Find how far a rider travels in 20 minutes, to two decimal places. (1 point)

Precalculus Unit Circle Test: questions 6–9

Question 6: Solving trigonometric equations (2 points)

Solve each equation for \(\theta\) in \([0,2\pi)\).

1. \(\cos\theta=-\frac{\sqrt{3}}{2}\) (1 point)
2. \(\tan\theta=1\) (1 point)

Question 7: Even and odd (2 points)

1. Find the exact value of \(\tan(-\frac{5\pi}{4})\). (1 point)
2. Decide whether \(f(x)=x^{2}\sin x\) is even, odd or neither, and justify. (1 point)

Question 8: Periodicity of sine (2 points)

The graph shows \(y=\sin x\) and \(\sin\frac{\pi}{6}=\frac{1}{2}\).

1. State the period of \(y=\sin x\). (1 point)
2. Find \(\sin\frac{13\pi}{6}\) and \(\sin(-\frac{7\pi}{6})\). (1 point)

Question 9: Unit circle coordinates (2 points)

The angle \(\theta\) lies in Quadrant II and \(\cos\theta=-\frac{8}{17}\).

1. Find \(\sin\theta\). (1 point)
2. Find \(\tan\theta\). (1 point)

How to use this precalculus unit circle test

Take this precalculus unit circle test without notes, then grade it with the test answer key out of 20 points.

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