Directed angles and radians
Answers are for parents and teachers.
1
State the quadrant of each angle: 100°, 300°, −20°, 480°.
100°: second. 300°: fourth. −20°: fourth. 480° = 360° + 120°: second.
2
Find the smallest positive measure of 1130° and of −500°.
1130 − 1080 = 50°. −500° + 720° = 220°.
3
Convert to radians: 30°, 150°, 300°.
π/6, 5π/6, 5π/3.
4
A circle has radius 30 m. Find the arc cut by π/6 radians, correct to 2 decimal places.
ℓ = π/6 × 30 = 5π ≈ 15.71 m.
5
An arc of 15 m lies on a circle of radius 6 m. Find its central angle in radians and in degrees.
θ = 15/6 = 2.5 rad ≈ 2.5 × 57.3° ≈ 143.2°.