6.1 Radian and Degree Measure

1. 6.1 Radian and Degree Measure Today we will learn the following topics: Terminology used to describe angles Degree measure of an angle Radian measure of an angle Converting between radian and degree measure

2. 6.1 Radian and Degree Measure Angles Trigonometry: measurement of triangles Angle Measure

3. 6.1 Radian and Degree Measure Standard Position Vertex at origin The initial side of an angle in standard position is always located on the positivex-axis.

4. 6.1 Radian and Degree Measure Positive and negative angles When sketching angles, always use an arrow to show direction.

5. 6.1 Radian and Degree Measure Measuring Angles The measure of an angle is determined by the amount of rotation from the initial side to the terminal side. There are two common ways to measure angles, in degrees and in radians. We’ll start with degrees, denoted by the symbol º. One degree (1º) is equivalent to a rotation of of one revolution.

6. 6.1 Radian and Degree Measure Classifying Angles Angles are often classified according to the quadrant in which their terminal sides lie. Ex1: Name the quadrant in which each angle lies. 50º 208º II I -75º III IV Quadrant 1 Quadrant 3 Quadrant 4

7. Radian MeasureA second way to measure angles is in radians. • Another way of measuring angles • Convenient because major measurements of a circle (circumference, area, etc.) are involve pi • Radians result in easier numbers to use

8. 6.1 Radian and Degree Measure Radian Measure

9. 6.1 Radian and Degree Measure Conversions Between Degrees and Radians • To convert degrees to radians, multiply degrees by • To convert radians to degrees, multiply radians by

10. Examples:

11. Ex 5. Convert the degrees to radian measure. 60 30 -54 -118 45

12. Ex 6. Convert the radians to degrees. a) b) c) d)

13. Class Work Convert from degrees to radians. 54 -300 Convert from radians to degrees. 3. 4.