How many of the following are matched correctly?
Degree measurement Radian 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
(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
Key steps: knowing the relation between degree measurement and radian measurement