1. 3.1 Radian Measure OBJ: Convert degree measure to radian measure Find trig values of angles expressed in radian measure

2. Conversions Factors 360  = 2  radians 180  =  radians 1  =  _ radians 180

3. DEF:  Converting Between  ‘s and Radians 2. Formula: FromToMultiply By DegreesRadians  180  Convert to Radians 45  240 

4. EX:  Convert to radians 45  45   180  45   180  4  4 240  240   180  4 240   3 180  44 3

5. 90 120 60 135 45 150 30 180 0 210 330 225 315 240 270 300

6. 90 120 60 135 45 150 30 180 0 210 330 225 315 240 270 300

7. º 0 30 45 60 90 120135150180210225240270300315 330 360 0 1 1  3 90 2 2  2  2 135 120 60 45 2 2  3 1 150 30 2 2 -1,0 180 0 1 0 210330 225 315 240 300 270 0 -1

8. º 0 90 180 270 360   0  

9. 00  2  3  2 22 º 0 90 180 270 360 0 1  2 -1,0  0  1 0 3  2 0-1

10. º 0 45 90 135 180 225 270 315 360     4  4 45 4    4 4, 4,   4  4 4

11. 00 4  2 3  4  5  4 3  2 7  4 2 2 º 0 45 90 135 180 225 270 315 360 2   2  2 3  4 1  2 2 4 45 4 4  0  8  4 4, 4, 5  7  4 6  4 4

12. º 6 6 6  6 30 6 0   6 6, 6 6 6 6 6 6 03060 90 120150 180180 210240 270270 300330 360

13. º 30 60 120 150 210 240 300 330 3 4 6 2 6 6 5 1  6 30 6 6 0  12  6 6, 6 7 11 6 6 8 9 10 6 6 6 00  6  3  2 2  3 5656  7676 4343 3  2 5  3 11  6 22 0 90 180270360

14.  00  6  4  3  2 2  3 3  4 5  6  7  6 5  4 4  3 3  2 5  3 7  4 11  6 22 º 0 30 45 60 90 120 135150 180210 225240 270 300 315 330 360 0 1 1  3  2 2 2  2   2  2 3  3 3  2 2 4 4 5    3 1 6 6 2 2 -1 0  0  1 0 7  11  6 6 5  7  4 4 4  3  7  3 2 3 0 -1

15. DEF:  Converting Between  ‘s and Radians 2. Formula: FromToMultiply By RadiansDegrees 180   ORReplace  With 180  Convert to degrees 11  6 5  4

16. DEF:  Converting Between  ‘s and Radians 2. Formula: FromToMultiply By RadiansDegrees 180   ORReplace  With 180  Convert to degrees 11  180  30 = 6  330  45 5  180  = 225  4  OR 5(180) = 5(45) = 4 225 

17. EX:  Convert to degrees 11  3 9494

18. EX:  Convert to degrees 11  3 11  180  3  11  180  60 3  660  99 4 9  180  4  9  180  45 4  405 

19. Special  ’s expressed in radians EX:  tan 2  3 EX:  csc 3  4

20. Special  ’s expressed in radians EX:  tan 2  3 tan 2  180  3  60 tan 2  180  3  tan 120  -  3 EX:  csc 3  4 2 2