Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
They begin with conversions and special angles, then use quadrants, arc length and a Ferris wheel. Give exact values unless a decimal is requested.
Standards: F-TF.A.1, F-TF.A.2, F-TF.C.8 · Level: Grade 11 Algebra 2
Problem 2 Radians to degrees ★★★
Convert 7π4 radians to degrees.
Problem 3 A radian measure without π ★★★
A dial on a machine turns through 4.2 radians. Express this turn in degrees, rounded to the nearest tenth.
Problem 4 Special angle in quadrant I ★★★
Find cos π3 and sin π3.
Problem 5 Reference angle in quadrant II ★★★
Find the coordinates of the unit-circle point at 5π6.
Problem 6 Quadrant III values ★★★
An angle of 4π3 radians is drawn in standard position. Name its quadrant and give its exact sine and cosine.
Problem 7 Tangent from coordinates ★★★
Find tan 3π4.
Problem 8 Read an angle on the unit circle ★★★
The unit circle shows five angles. Give the exact coordinates of the point at 5π/3 (300°).
Problem 9 Negative angle ★★★
Find sin(−π/4) and cos(−π/4).
Problem 10 Arc length of a sector ★★★
A sector has radius 8 inches and central angle 5π/12. Find the arc length, exactly and to the nearest hundredth.
Problem 11 Coterminal angle ★★★
Name the angle in the interval [0, 2π) that has the same terminal side as 23π/4, and state its sine.
Problem 12 Point on the unit circle ★★★
The point P(−3/5, y) is on the unit circle in quadrant II. Find y, then sin, cos and tan of the angle.
Problem 13 Cosine from sine, quadrant II ★★★
Suppose sin θ = 5/13 and θ is in quadrant II. Find cos θ and tan θ.
Problem 14 Sine from cosine, quadrant IV ★★★
Suppose cos θ = 8/17 and θ is in quadrant IV. Find sin θ and tan θ.
Problem 15 Sine and cosine from tangent ★★★
Suppose tan θ = 7/24 and θ is in quadrant III. Find sin θ and cos θ.
Problem 16 Ferris wheel position ★★★
A Ferris wheel has radius 25 feet. Place its center at the origin. A rider starts at the rightmost point and rotates counterclockwise by 5π/4. Find the rider’s horizontal and vertical distances from the center, to the nearest hundredth.
Problem 17 Distance traveled by a clock hand ★★★
A minute hand is 9 inches long. In 40 minutes, through what angle in radians does it turn, and how far does its tip travel? Give the distance to the nearest hundredth.
Problem 18 Show an identity ★★★
Show that (sin θ + cos θ)2 = 1 + 2 sin θ cos θ.
Problem 19 Two-step ratio problem ★★★
Suppose cos θ = −√5/3 and θ is in quadrant II. Find sin θ and tan θ exactly.
Problem 20 Can both values be true? ★★★
Justify whether any angle θ can have sin θ = 0.6 and cos θ = 0.7.
