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Question

Match the following angles in radians with their corresponding angles in degrees.

A
75
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B
315
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C
571724′′
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D
220
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Solution

We know the relation:
D180=Rπ

D=180×Rπ
Where R is the angle in radians and D is the angles in degrees.
(a) R=1 radiansD=180×1π
R=180π=57.29
Now, 57.29=57+0.29
0.29=0.29×60=17.40=17+0.4
0.4=0.4×60′′=24′′
1 radian=571724′′

(b) 5π12D=180×5π12×π
D=180×512=75

(c) 7π4D=180×7π4×π
D=180×74=315

(d) 11π9D=180×11π9×π
D=180×119=220

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