Question

How many of the following are matched correctly?

$\begin{array}{cc}\text{Degree measurement}& \text{Radian measurement}\\ \text{(A)}{180}^{\circ }& \text{(1)}\pi \\ \text{(B)}{60}^{\circ }& \text{(2)}\frac{\pi }{6}\\ \text{(C)}{0}^{\circ }& \text{(3)}0\\ \text{(D)}{120}^{\circ }& \text{(4)}2\frac{\pi }{6}\\ \text{(E)}{360}^{\circ }& \text{(5)}2\pi \\ \text{(F)}{30}^{\circ }& \text{(6)}\frac{\pi }{3}\\ \text{(G)}{90}^{\circ }& \text{(7)}\frac{\pi }{2}\\ \text{(H)}{45}^{\circ }& \text{(8)}\frac{\pi }{4}\\ \text{(I)}{270}^{\circ }& \text{(9)}3\pi \end{array}$
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Answer 1

To solve this, we should know the relation between degree and radian. We know that one right - angle is equal to $\frac{\pi }{2}$ radian or ${90}^{\circ }$.

$\Rightarrow {90}^{\circ }=\frac{\pi }{2}\text{radian}$
$\Rightarrow 1^{\circ }=\frac{\pi }{180}\text{radian}$

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

$\Rightarrow x^{\circ }=x\times \frac{\pi }{180}\text{radian}$
$\text{(A)}{180}^{\circ }=180\times \frac{\pi }{180}=\pi \text{radian}$
$\text{(B)}{60}^{\circ }=60\times \frac{\pi }{180}=\frac{\pi }{3}\text{radian}$
$\text{(C)}{0}^{\circ }=0\times \frac{\pi }{180}=0\text{radian}$
$\text{(D)}{120}^{\circ }=120\times \frac{\pi }{180}=\frac{2\pi }{3}\text{radian}$
$\text{(E)}{360}^{\circ }=360\times \frac{\pi }{180}=2\pi \text{radian}$
$\text{(F)}{30}^{\circ }=30\times \frac{\pi }{180}=\frac{\pi }{6}\text{radian}$
$\text{(G)}{90}^{\circ }=90\times \frac{\pi }{180}=\frac{\pi }{2}\text{radian}$
$\text{(H)}{45}^{\circ }=45\times \frac{\pi }{180}=\frac{\pi }{4}\text{radian}$
$\text{(I)}{270}^{\circ }=270\times \frac{\pi }{180}=\frac{3\pi }{2}\text{radian}$