Question

How do you convert 73 degrees to radians?

Answer 1

Hint: Here in this question, we have to convert degrees into radians. We should know that 360 degrees = $2\pi$ radians. If we wish to convert any given angle from the measure of degrees to radians, the value has to be multiplied by ${\displaystyle \frac{\pi }{180}}$ . Also need to know that an angle that is subtended at the centre by an arc having a length equal to the radius of the circle.

Let’s solve the question now.

Let us make a circle and assume ‘R’ as a radius of a circle and draw the arc of the same length ‘R’. When an angle $\theta$ is subtended at the centre by an arc length equal to the radius of the circle, then the angle is said to be one radian.

From the above figure, if we wish to find $\theta$, we divide arc length ‘S’ with the radius such that:
 $\Rightarrow \theta ={\displaystyle \frac{S}{R}}$
One Revolution of a circle is equal to ${360}^{\circ }$ which is equal to $2\pi$ radians.
 $\Rightarrow {360}^{\circ }=2\pi$ radians
Now if ${360}^{\circ }=2\pi$ radians and if we divide both sides by 2, we will get:
 $\Rightarrow {\displaystyle \frac{{360}^{\circ }}{2}}={\displaystyle \frac{2\pi }{2}}$
After reducing the terms, we will get:
 $\Rightarrow {180}^{\circ }=\pi$ Radians
This is the conversion which we will be using to convert degrees to radians.
If we wish to convert any degree into radian, we have to multiply the degree with a factor of ${\displaystyle \frac{\pi }{{180}^{\circ }}}$ . So let’s convert 73 degrees to radians.
First, multiply 73 with ${\displaystyle \frac{\pi }{{180}^{\circ }}}$ :
 $\Rightarrow 73\times {\displaystyle \frac{\pi }{{180}^{\circ }}}$
Now, take $\pi =3.14$ :
 $\Rightarrow 73\times {\displaystyle \frac{3.14}{{180}^{\circ }}}$
The next step is to multiply 73 with 3.14, we will get:
 $\Rightarrow {\displaystyle \frac{229.22}{{180}^{\circ }}}$
Now, after dividing the value in radians will be:
 $\Rightarrow 1.2734$ radians.
So this is our final answer.

Note:
There is an alternative method for this question. As we know that degrees and radians are based on equality i.e. ${360}^{\circ }=2\pi$ radians. As the value of degrees will reduce, corresponding to it radians will also get reduced. So this is the situation of direct proportion and can be solved by this method too. The degree is given i.e. 73 and the let radians for this degree be ‘x’. so we can write it as:
 $\Rightarrow {\displaystyle \frac{{360}^{\circ }}{2\pi }}={\displaystyle \frac{{73}^{\circ }}{x}}$
Now we have to solve for ‘x’. We will cross multiply:
 $\Rightarrow {360}^{\circ }\times x={73}^{\circ }\times 2\pi$
Next is to keep ‘x’ alone and take all the terms to the other side. We get:
 $\Rightarrow x={\displaystyle \frac{{73}^{\circ }\times 2\pi }{{360}^{\circ }}}$
Put x = 3.14, we get:
 $\Rightarrow x={\displaystyle \frac{{73}^{\circ }\times 2\times 3.14}{{360}^{\circ }}}$
On solving further we will get:
 $\Rightarrow x={\displaystyle \frac{458.44}{{360}^{\circ }}}$
On dividing, we get:
 $\Rightarrow x=1.2734$ radians