Question

$x^{\circ }=$ radian and $x$ radian $=$ degree

• A. $\frac{180}{\pi }\times x$
• B. $\frac{360}{\pi }\times x$
• C. $\frac{\pi }{360}\times x$
• D. $\frac{180}{\pi }\times \frac{1}{x}$
• E. $\frac{\pi }{180}\times x$

Answer 1

Answer: (A), (E)

The correct options are
A $\frac{180}{\pi }\times x$
E $\frac{\pi }{180}\times x$

First we will express a known angle in degree and radian and equate both. For this you can consider any angle whose degree and radian measurements are known.
For example, right-angle is ${90}^{\circ }$ and $\frac{\pi }{2}$ radian

$\Rightarrow {90}^{\circ }=\frac{\pi }{2}$ radian
$\Rightarrow 1^o=\frac{\pi }{180}$ radian
$\Rightarrow x^{\circ }=x\times \frac{\pi }{180}$ radian.
To get the next relation,
$\frac{\pi }{2}$ radian $={90}^{\circ }$
$\Rightarrow 1$ radian $=\frac{{180}^{\circ }}{\pi }$
$\Rightarrow x$ radian $=\frac{180}{\pi }\times x$ degree