Question

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

Answer 1

Hint: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.