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
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