Radian and Degree Measure

Radian Measure• A radian is the measure of a central angle

that intercepts an arc length equal to the radius of the circle

• Radians measure the amount of rotation from the initial side to the terminal side of an angle

Converting degrees to radians

• Multiply the degree by• DO NOT type the π into the calculator! Type in the

fraction and use MATH 1: Frac to reduce. Your answer must have a pi symbol!

• Examples: Convert to radians– 38°

– -224°

– 126°

180

1

Converting radians to degrees

• Multiply by• The pi symbols should cancel out. You do NOT

have to type the pi symbol into your calculator since it will cancel.

• Remember to put a degree symbol in your answer!

• Examples: Convert to degrees

180

5

28

Radians without π

• Any angle measure WITHOUT a degree symbol is in radian measure!!

Convert 2 radians to degrees

180

2

This is the only time you should type the pi symbol into your calculator!2(180/π)The pi symbol is under 2nd ^

Complementary angles

• Angles whose sum is 90ßor Ä/2

Angles larger than 90ß (1.57 radians) do NOT have a complement

Example: Find the complement of each angle:

a.) 62 b.) Ä/5 c.) 2 radians

Supplementary angles

• Angles whose sum is 180ß

Examples: Find the supplement of each angle

a.) 112ß b.) 31ß c.) 31Ä/36

Coterminal Angles

• Standard position- vertex at the origin and the terminal side rotates to form an angle

• All angles can be measured in a clockwise AND counter-clockwise direction

Finding coterminal angles

• In degrees, add and/or subtract 360

• In radians, add and/or subtract 2Ä (remember do NOT put the Ä symbol into your calculator)

• Examples: Find one positive and one negative coterminal angle

a.) 116ß b) 5Ä/11