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
P 19 EX3a: Convert 74 8 14 to decimal degrees (Unit 5 p 1)74 8 1474 +
8
60 +
14
3600 =
74.137
P22:30 Convert to Dec. Deg.(HW 5.1)
165 51 09165 +
51
60 +
9
3600 =
165.853
P22: 36 Convert to DMS (HW 5.1)
122.6853
.6853 • 60 =41.118
.118 • 607.08 122 41 07
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
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
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
cos .514
cos .5149
.870
cos 3.14 = .523
6 6
cos 30°
.87
cot 1.3206
cot 1.3206
1/tan(1.3206)
.256
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
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
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