Question

What is $\dfrac{17\pi }{12}$radians in degrees?

Answer 1

Before solving this, we are going to know about the basic definitions of radians and degrees and how to convert the given radians into degrees.

Complete step-by-step solution:
Radians and degrees are the two different elements which are used in the measurement of the angles. While measuring the angles in a geometry, we probably use the conversion of degrees to radians. The measure of the angle is denoted by degree, with symbol .
Let us know the Radian to Degree conversion
We know that the value of ${{180}^{\circ }}$equals to $\pi$ radians. For converting any given angle which is in degrees to the radians, we need to multiply the value by $\dfrac{\pi }{{{180}^{\circ }}}$.
Similarly, for converting the given radian into degree, we need to multiply it with $\dfrac{{{180}^{\circ }}}{\pi }$ .
The $\pi$ value is $22/7$ or $3.14$.
The simple formula to change the degree to radian is given as follows
$\text{Degree}\times \text{ }\dfrac{\pi }{{{180}^{\circ }}}=\text{ radians}$
For converting radians to degrees, we need to know
$2\pi \text{ radians = 360 degrees for one full revolution}$
Now, dividing with 2 on both sides, we get
$\pi \text{ radians = 180 degrees}$
We shall now divide by $\pi$ on both sides,
$\Rightarrow \text{1 radians = }\dfrac{180}{\pi }\text{ degrees}$
Given question is to convert $\dfrac{17\pi }{12}$radians in degrees, so
$\Rightarrow \dfrac{17\pi }{12}\text{ radians = }\dfrac{17\pi }{12}\times \dfrac{{{180}^{\circ }}}{\pi }$
On cancelling $\pi$ on right side and simplify, we get
$\therefore \dfrac{17\pi }{12}\text{ radians = 255 degrees}$.

Note: A radian is a unit of measure of angles. Simply, one radian is the angle made by the centre of a circle by an arc whose length is equal to the radius of the circle. A degree is also a measure of an angle, one degree is $\dfrac{1}{{{360}^{th}}}$part of a full circle.