Pre-Calculus Study Guide: Radians,
Degrees, Angles & Arc Length
Core Concepts
A circle contains 360° or 2π radians.
90° = π/2, 180° = π, 270° = 3π/2, 360° = 2π.
Convert degrees→radians: degrees × π/180.
Convert radians→degrees: radians × 180/π.
Common Angle Measures
30°=π/6
45°=π/4
60°=π/3
90°=π/2
135°=3π/4
150°=5π/6
180°=π
270°=3π/2
315°=7π/4
360°=2π
Complementary & Supplementary
Complementary angles sum to 90° (π/2).
Supplementary angles sum to 180° (π).
Coterminal Angles
Add or subtract 360° (or 2π radians) to find coterminal angles.
Determine the quadrant using the positive coterminal angle if needed.
Standard Position
Initial side lies on the positive x-axis.
Positive angles rotate counterclockwise.
Negative angles rotate clockwise.
Degrees, Angles & Arc Length
Core Concepts
A circle contains 360° or 2π radians.
90° = π/2, 180° = π, 270° = 3π/2, 360° = 2π.
Convert degrees→radians: degrees × π/180.
Convert radians→degrees: radians × 180/π.
Common Angle Measures
30°=π/6
45°=π/4
60°=π/3
90°=π/2
135°=3π/4
150°=5π/6
180°=π
270°=3π/2
315°=7π/4
360°=2π
Complementary & Supplementary
Complementary angles sum to 90° (π/2).
Supplementary angles sum to 180° (π).
Coterminal Angles
Add or subtract 360° (or 2π radians) to find coterminal angles.
Determine the quadrant using the positive coterminal angle if needed.
Standard Position
Initial side lies on the positive x-axis.
Positive angles rotate counterclockwise.
Negative angles rotate clockwise.
