Question

if an angle measures D degree s or C radians show that D/90=2c/π​

Answer 1

Given:

The measurement of angle = $D^\circ$ or C radians

To Prove:

$\dfrac{D}{90} = \dfrac{2C}{\pi}$

First of all, let us have a look at the relation between degrees and radians.

Suppose we have any arc subtending an angle $\theta$ on center of the circle.

If we keep on increasing this angle $\theta$ and complete the whole circle, it will cover the the circumference i.e. $2 \pi r$ and complete circle covers an angle of $360^\circ$.

Let us assume that the circle is of unit circle:

Then, 2$\pi$ radians = $360^\circ$

$\Rightarrow \pi\ radians = 180^\circ$

We are given an angle of  $D^\circ$ or C radians

Let us convert $D^\circ$ it to radians and compare it to C:

$180^\circ = \pi\ radian$

$1^\circ = \dfrac{\pi}{180}\ radian$

$D^\circ = \dfrac{\pi}{180} \times D$ radians

$\Rightarrow C = \dfrac{\pi}{180} \times D\\\Rightarrow \dfrac{2C}{\pi} = \dfrac{D}{90}$

Hence proved that:

$\dfrac{D}{90} = \dfrac{2C}{\pi}$