Question

How do you convert negative radians to degrees?

Answer 1

Hint: There are two units of measure for an angle. One is called degree (denoted by $${}^{\circ }$$ sign). And the other unit of measure is radian, radian is denoted by rad but it is not denoted by using this notation generally. Every angle can either be measured in degree or radian. The measure of angles can also be converted from one unit to another unit. The conversion formula is as follows:
From degree to radian – measure of angle in degree $$\times {\displaystyle \frac{\pi }{180{}^{\circ }}}$$ .
From radian to degree – measure of angle in radian $$\times {\displaystyle \frac{180{}^{\circ }}{\pi }}$$.

Complete step by step answer:
When two lines intersect, they give rise to four different spaces for the point of intersection. These created spaces are called angles. If the rotation is anticlockwise then the angles are said to be positive, and if the rotation is clockwise then the angles are said to be negative. When an object moves through a complete cycle, we say it has covered 360 degrees (360$${}^{\circ }$$). Similarly, a radian is an angle made at the center of the circle by an arc that is equal to the length of the radius of that particular circle. From these two definitions, we can say that,
One rotation$$=360{}^{\circ }=2\pi$$
$$\Rightarrow 360{}^{\circ }=2\pi$$
Dividing both sides by $$2\pi$$, we get
$$\begin{array}{rl}& \Rightarrow {\displaystyle \frac{360{}^{\circ }}{2\pi }}={\displaystyle \frac{2\pi }{2\pi }}\\ & \Rightarrow 1rad={\displaystyle \frac{180{}^{\circ }}{\pi }}\end{array}$$
From this, we can state the formula for radian to degree conversion as,
Measure of angle in degree = Measure of angle in radian $$\times {\displaystyle \frac{180{}^{\circ }}{\pi }}$$. This formula is applicable for both positive as well as negative angles.

Note:
This conversion formula should be remembered, as it might become useful in some questions of trigonometry, coordinate geometry etc. Also, its inverse, that is, conversion from radian to degree should be remembered.