1. Warm up for 8.5 Compare the ratios sin A and cos B Compare the ratios sec A and csc B Compare the ratios tan A and cot B pg 618

2. At an altitude of 1,000 ft., a balloonist measures the angle of depression from the balloon to the landing zone. The measure of the angle is 15 degrees. How far is the balloon from the landing zone? Angle of Depression Pg 622

3. 3 Radian and Degree Measure In this section, we will study the following topics: Terminology used to describe angles Degree measure of an angle Radian measure of an angle Converting between radian and degree measure Find coterminal angles Lots of room for notes on 623

4. Radian and Degree Measure 4 Angles Trigonometry: measurement of triangles Angle Measure

5. Radian and Degree Measure 5 Standard Position Vertex at origin The initial side of an angle in standard position is always located on the positive x-axis.

6. Radian and Degree Measure 6 Positive and negative angles When sketching angles, always use an arrow to show direction.

7. Radian and Degree Measure 7 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.

8. Radian and Degree Measure Radian and Degree Measure 8 Measuring Angles

9. Radian and Degree Measure 9 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 Classifying Angles Quadrant 1 Quadrant 3 Quadrant 4

10. Radian and Degree Measure 10 Classifying Angles Standard position angles that have their terminal side on one of the axes are called quadrantal angles. For example, 0º, 90º, 180º, 270º, 360º, … are quadrantal angles.

11. Radian and Degree Measure 11 Radian Measure A second way to measure angles is in radians. Definition of Radian: One radian is the measure of a central angle  that intercepts arc s equal in length to the radius r of the circle. In general,

12. Radian and Degree Measure Radian and Degree Measure 12 Radian Measure

13. Radian and Degree Measure Radian and Degree Measure 13 Radian Measure

14. Radian and Degree Measure Radian and Degree Measure 14 Conversions Between Degrees and Radians 1. To convert degrees to radians, multiply degrees by 2. To convert radians to degrees, multiply radians by

15. Ex 5. Convert the degrees to radian measure. a) 60 b) 30 c) -54 d) -118 e) 45

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

17. 17 0°  360 °  30 °  45 °  60 °  330 °  315 °  300 °   120 °  135 °  150 °  240 °  225 °  210 °  180 ° 90 °  270 °   Degree and Radian Form of “Special” Angles

18. Class Work Convert from degrees to radians. 1. 54 2. -300 Convert from radians to degrees. 3. 4.

19. 8.5 and Angles and Angle Measure Worksheet 19