Radians and the Unit Circle: Algebra 2 Math Test – PDF Download

Question 1: Converting angle measures (2 points)

Complete each conversion.

1. Write \(150^{\circ}\) in radians, in terms of \(\pi\). (1 point)
2. Write \(\frac{7\pi}{4}\) radians in degrees. (1 point)

Question 2: Arc length and angle (2 points)

A sector has radius 9 inches and central angle \(\frac{2\pi}{3}\).

1. Find the exact arc length. (1 point)
2. On a different circle of radius 8 inches, an arc is 12 inches long. Find its central angle in radians. (1 point)

Question 3: Point on the unit circle (2 points)

The terminal side of an angle of \(\frac{7\pi}{6}\) radians is shown.

Find the exact coordinates of the point where it meets the unit circle. (2 points)

Question 4: Exact sine and cosine (2 points)

Find the exact value of each.

1. \(\sin\frac{5\pi}{3}\) (1 point)
2. \(\cos\frac{3\pi}{4}\) (1 point)

Question 5: Tangent values (2 points)

Find the exact value of each.

1. \(\tan\frac{7\pi}{4}\) (1 point)
2. \(\tan\frac{2\pi}{3}\) (1 point)

Question 6: Solving a sine equation (2 points)

Find all angles \(\theta\) with \(0\le\theta< 2\pi\) such that \(\sin\theta=-\frac{1}{2}\).

Question 7: Sine and tangent from cosine (2 points)

The terminal side of \(\theta\) is in Quadrant II and \(\cos\theta=-\frac{12}{13}\).

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

Question 8: Using symmetry (3 points)

The angle \(\theta\) satisfies \(\pi<\theta<\frac{3\pi}{2}\) and \(\sin\theta=-\frac{4}{5}\).

1. Find \(\cos\theta\). (1 point)
2. Find \(\tan\theta\). (1 point)
3. Find \(\sin(-\theta)\) and \(\cos(-\theta)\). (1 point)

Question 9: Ferris wheel (3 points)

A Ferris wheel has radius 20 feet and center 25 feet above the ground. A rider’s height is \(h=25+20\sin\theta\) feet.

1. Find \(h\) when \(\theta=\frac{\pi}{6}\). (1 point)
2. Find \(h\) when \(\theta=\frac{4\pi}{3}\) to the nearest hundredth. (1 point)
3. Find all \(\theta\) with \(0\le\theta< 2\pi\) for which \(h=15\). (1 point)

⬇ Download the Algebra 2 Radians and the Unit Circle test (PDF, 95 KB)

See every chapter on the Algebra 2 math page.