Radians and Unit Circle Test – Algebra 2 Math (Printable PDF)

Question 1 Convert angle measures (2 points)

1. Convert 210° to radians. (1 point)
2. Convert 5π/9 radians to degrees. (1 point)

Question 2 Exact values (3 points)

Find the exact value.

1. sin(2π/3) (1 point)
2. cos(5π/4) (1 point)
3. tan(11π/6) (1 point)

Question 3 Read the unit circle (3 points)

The point shown is on the unit circle.

1. Find the angle θ in radians, 0 < θ < 2π. (1 point)
2. Give sin θ, cos θ and tan θ. (2 points)

Question 4 Arc length (2 points)

A circle has radius 14 feet. Find the length of the arc cut off by a central angle of 11π/18. Give the exact value and the value to the nearest hundredth.

Question 5 Ratios from a given sine (2 points)

Suppose sin θ = −9/41 and θ is in quadrant III. Find cos θ and tan θ.

Question 6 Ratios from a given cosine (2 points)

Suppose cos θ = −√7/4 and θ is in quadrant II. Find sin θ and tan θ exactly.

Question 7 Coterminal angles (2 points)

Find the exact value of cos(19π/6).

Question 8 Verify an identity (2 points)

Show that (1 − cos θ)(1 + cos θ) = sin² θ.

Question 9 Ferris wheel (2 points)

A Ferris wheel has radius 40 feet. A rider starts at the rightmost point and rotates counterclockwise by 2π/3. How far above the horizontal line through the center is the rider? Give an exact value and a decimal to the nearest tenth.