3.1 radian measure obj: convert degree measure to radian measure find trig values of angles...

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

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

3.1 Radian Measure

OBJ: Convert degree measure to radian measure Find trig values of angles expressed in radian measure

Page 2: 3.1 Radian Measure OBJ: Convert degree measure to radian measure Find trig values of angles expressed in radian measure

P 19 EX3a: Convert 74 8 14 to decimal degrees (Unit 5 p 1)74 8 1474 +

8

60 +

14

3600 =

74.137

Page 3: 3.1 Radian Measure OBJ: Convert degree measure to radian measure Find trig values of angles expressed in radian measure

P22:30 Convert to Dec. Deg.(HW 5.1)

165 51 09165 +

51

60 +

9

3600 =

165.853

Page 4: 3.1 Radian Measure OBJ: Convert degree measure to radian measure Find trig values of angles expressed in radian measure

P22: 36 Convert to DMS (HW 5.1)

122.6853

.6853 • 60 =41.118

.118 • 607.08 122 41 07

Page 5: 3.1 Radian Measure OBJ: Convert degree measure to radian measure Find trig values of angles expressed in radian measure

DEF: Converting Between ‘s and Radians

Convert to degrees4.2 • 180( = 3.14) (2 = 6.28)240.642(180°-360°)Convert to radians29 40 • (30° = ) 180 6.518 (3.14/6=.523 )74.9162°•(60=/3= 180 1.0471.308(90=/2=1.57)

2. Formula:

From To Multiply By

Radians Degrees 180

Degrees Radians

180

Page 6: 3.1 Radian Measure OBJ: Convert degree measure to radian measure Find trig values of angles expressed in radian measure

EX: Find sin (74 8 14)(Unit 5p1)

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

Page 7: 3.1 Radian Measure OBJ: Convert degree measure to radian measure Find trig values of angles expressed in radian measure

EX:Find csc(165 5109)(Unit5p1)

1_______

sin (165.853)4.091

csc 0 Øcsc 30 2

csc 60 1.2

csc 90 1

csc 120 1.2

csc 150 2

(sin 166 = .25 or )csc 180 Ø

Page 8: 3.1 Radian Measure OBJ: Convert degree measure to radian measure Find trig values of angles expressed in radian measure

cos .514

cos .5149

.870

cos 3.14 = .523

6 6

cos 30°

.87

Page 9: 3.1 Radian Measure OBJ: Convert degree measure to radian measure Find trig values of angles expressed in radian measure

cot 1.3206

cot 1.3206

1/tan(1.3206)

.256

Page 10: 3.1 Radian Measure OBJ: Convert degree measure to radian measure Find trig values of angles expressed in radian measure

P80: 32) sin = .2784 (HW 5.1)

sin = .2784

sin-1 sin = sin-1.2784

= sin-1 (.2784)

16.165

sin 0 0

sin 30 .5

Page 11: 3.1 Radian Measure OBJ: Convert degree measure to radian measure Find trig values of angles expressed in radian measure

P80: 34) cot = 1.257 (HW 5.1)

cot = 1.257tan = 1

1.257tan-1 tan = tan-1 1

1.257 = tan-1 ( 1__

1.257) 38.504º

Page 12: 3.1 Radian Measure OBJ: Convert degree measure to radian measure Find trig values of angles expressed in radian measure

cos s = .0581 sec s = 2.1234

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