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3.1 Radian Measure

3.1 Radian Measure. OBJ: Convert degree measure to radian measure Find trig values of angles expressed in radian measure. P 19 EX 3a :  Convert 74  8  14  to decimal degrees (Unit 5 p 1). 74  8  14  74 + 8 60 + 14 3600 = 74.137 .

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3.1 Radian Measure

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

  2. P 19 EX3a:Convert 74 8 14 to decimal degrees (Unit 5 p 1) 74 8 14 74 + 8 60 + 14 3600 = 74.137

  3. P22:30 Convert to Dec. Deg.(HW 5.1) 165 51 09 165 + 51 60 + 9 3600 = 165.853

  4. P22: 36 Convert to DMS (HW 5.1) 122.6853 .6853 • 60 = 41.118 .118 • 60 7.08 12241 07

  5. DEF:Converting Between  ‘s and Radians 2. Formula: Convert to degrees 4.2 • 180( = 3.14)  (2 = 6.28) 240.642(180°-360°) Convert to radians 29 40 •  (30° = ) 180 6 .518 (3.14/6=.523 ) 74.9162°•(60=/3= 180 1.047 1.308(90=/2=1.57)

  6. sin (74.137) .962 sin 0 0 sin 30 .5 sin 60 .87 sin 90 1 sin 120 .87 sin 150 .5 (sin166) .25 sin 180 0 EX: Find sin (74 8 14)(Unit 5p1)

  7. 1_______ sin (165.853) 4.091 csc 0 Ø csc 30 2 csc 60 1.2 csc 90 1 csc 120 1.2 csc 150 2 (sin 166 = .25 or ) csc 180 Ø EX:Find csc(165 5109)(Unit5p1)

  8. cos .5149 .870 cos 3.14 = .523 6 6 cos 30° .87 cos .514

  9. cot 1.3206 1/tan(1.3206) .256 cot 1.3206

  10. sin  = .2784 sin-1 sin  = sin-1.2784  = sin-1 (.2784) 16.165 sin 0 0 sin 30 .5 P80: 32) sin  = .2784 (HW 5.1)

  11. P80: 34) cot  = 1.257 (HW 5.1) cot  = 1.257 tan  = 1 1.257 tan-1 tan  = tan-1 1 1.257  = tan-1 ( 1__ 1.257) 38.504º

  12. cos s = .0581 cos-1 cos s = cos-1.0581 s = cos-1(.0581) 1.513 (3.14/2 = 1.571) Degree Measure cos-1(0) 90 (90 = /2 = 3.14/2) sec s = 2.1234 cos-1cos s =cos-11/2.1234 s = cos-1(1/2.1234) 1.080 cos s = .0581 sec s = 2.1234

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