Question

How do you convert $37$ degrees to radian?

Answer 1

Hint: Here, the question is to convert the given degrees in radian. Conversion of degrees to radian and radians to degrees are very simple to the extent of the given formulas. By using the formula we will be able to find the correct answer faster.

Formula used: For converting from degrees to radians we use,
angle in degrees\[ \times \dfrac{\pi }{{180}}\]
For converting from radians to degrees,
\[{\text{angle in radians}} \times \dfrac{{180}}{\pi }\]

Complete step-by-step solution:
In this question, we are asked to convert $37$ degrees to radian.
We will do this by using the above mentioned formula.
For any value of angles, let the angle be $x$ degrees then, converting from degrees to radians we will use, \[x \times \dfrac{\pi }{{180}}\]
If we need to convert from radians to degrees, let the angle be $y$ in radians then \[y \times \dfrac{{180}}{\pi }\]
Now, since we have to convert $37$ degrees to radian we will use the first one
That is for converting from degree to radians we use, \[x \times \dfrac{\pi }{{180}}\]
So here $x = {37^ \circ }$
Substituting $x = 37$ in the formula \[x \times \dfrac{\pi }{{180}}\]
\[ \Rightarrow 37 \times \dfrac{\pi }{{180}}\]
We know that the default value of $\pi $ is $3.14$
\[ \Rightarrow 37 \times \dfrac{{3.14}}{{180}}\]
Let us multiply the term and we get,
\[ \Rightarrow \dfrac{{116.18}}{{180}}\]
On divide the term and we get,
$ \Rightarrow 0.645$

Therefore the radian value of ${37^ \circ }$ is $0.645$

Note: One way to remember these formulas is to think of this way:
If we want to find something in radians and the value is given in the degrees,
As we know, ${180^ \circ }$ is or can be represented as$\pi $,$180$ degrees = $\pi $
Now, we need to convert the given value in radians which is $x$,$37$ degrees = $x$
We can simply cross multiply both the ones,

\[{180^ \circ }\]	\[\pi \]
\[{37^ \circ }\]	\[x\]

Cross multiplying,
$ \Rightarrow 180x = 37\pi $
On putting the value of \[\pi \]and we get
$ \Rightarrow 180x = 37 \times 3.14$
On divide \[180\] on both sides and we get
$ \Rightarrow x = \dfrac{{37 \times 3.14}}{{180}}$
Therefore the radian value of ${37^ \circ }$ is $0.645$.