1. Degrees and Radians
Pre-Calculus
Keeper 11

2. Angle

3. Angular Unit of Measure
The most common angular unit of measure is the degree (°), which is equivalent to of a full rotation (clockwise) about the vertex. Degree measure can also be expressed using decimal degree form or degree-minute- second (DMS) form where each degree is subdivided into 60 minutes (‘) and each minute is subdivided into 60 seconds (“).

4. Convert Between DMS and Decimal Degree Form
Convert to decimal degree or DMS (appropriately) ° 32° 5 ′ 28"

5. Radian Measure
The measure of 𝜃 in radians of a central angle of a circle is equal to the ratio of the length of the intercepted arc s to the radius r of the circle.
Degree/Radian conversion Rules
To convert a degree measure to radians, multiply by 𝜋 𝑟𝑎𝑑𝑖𝑎𝑛𝑠 180° .
To convert a radian measure to degree, multiply by 180° 𝜋 𝑟𝑎𝑑𝑖𝑎𝑛𝑠 .

6. Convert Between Degree and Radian Measure
120°
−45°
5𝜋 6
− 3𝜋 2

7. Coterminal Angles
Two angles can have the same initial and terminal sides but different measures. Such angles are called coterminal angles.

8. Coterminal Angles Degrees Radians
If the angle is measured in degrees then add or subtract multiples of 360.
If the angle is measured in radians then add or subtract multiples of 2𝜋.

9. Find one positive and one negative angle coterminal with the given angle.
b. − 𝜋 3

10. Sums of Angles
Complementary Angles Two acute angles are complementary if their sum is 90º.
Supplementary Angles Two acute angles are supplementary if their sum is 180º.

11. Example – Complementary and Supplementary Angles
Find the Complement and the Supplement of o
Find the Complement and the Supplement of 𝜋 6