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Question

How many of the following are matched correctly?

Degree measurementRadian measurement(A)180(1)π(B)60(2)π6(C)0(3)0(D)120(4)2π6(E)360(5)2π(F)30(6)π3(G)90(7)π2(H)45(8)π4(I)270(9)3π
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Solution

To solve this, we should know the relation between degree and radian. We know that one right - angle is equal to π2 radian or 90.

90=π2radian
1=π180radian

From this relation we can convert all the degree measurements into radian.

x=x×π180 radian
(A) 180=180×π180=π radian
(B) 60=60×π180=π3 radian
(C) 0=0×π180=0 radian
(D) 120=120×π180=2π3 radian
(E) 360=360×π180=2π radian
(F) 30=30×π180=π6 radian
(G) 90=90×π180=π2 radian
(H) 45=45×π180=π4 radian
(I) 270=270×π180=3π2 radian


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