Question

How do you convert $35$ degrees into radians?

Answer 1

Hint: In this problem we have to convert $35$ degrees into radians. We have the relation between the radians and degrees as $1{}^\circ =\dfrac{\pi }{180}$ radians. We will use the above formula and simplify the equation to get the result.

Formula used:
1. $1{}^\circ =\dfrac{\pi }{180}$

Complete step by step solution:
Given that, to convert $35$ degrees into radians.
We have the formula $1{}^\circ =\dfrac{\pi }{180}$.
To convert $35$ degrees into radians, we will multiply the above equation with $35$ on both sides of the above equation, then we will get
$35\times 1{}^\circ =35\times \dfrac{\pi }{180}$
Simplifying the above equation, we will get
$35{}^\circ =\dfrac{7\pi }{36}$
Hence the value of $35{}^\circ $ in radians is $\dfrac{7\pi }{36}$.
If you use the value $\pi =3.14$ in the above equation, then we will get
$\therefore 35{}^\circ \simeq 0.61$ radians.


Additional Information:
Let's look into the terms Degree and Radian.
Degree: A degree, a degree of arc or arc degree is a measurement of plane angle. The symbol for degree is $\left( ^{\circ } \right)$. One degree is equal to $\dfrac{\pi }{180}$ radians.
Radian: the radian is the standard unit of angle which is defined as the ratio between the length of an arc and its radius. One radian is approximately equal to $57.3$ degree. its symbol is radian, an alternative symbol is the superscript letter $C$ which is infrequently used as it can be easily mistake for a degree symbol $\left( ^{\circ } \right)$

Note:
In this problem they have asked to convert the degrees into radians, so we have used the equation $1{}^\circ =\dfrac{\pi }{180}$. If they have asked to convert the radians into degrees from the above relation, we can write $\pi =180{}^\circ $. We will use this formula and simplify the equation to get the result.