Question

How do you convert radian measures to degrees?

Answer 1

Hint: We need to know the basic formula for converting the radian measures into degrees. For understanding that we can make an example question. If they give any radian values in the question, we would involve the operation of addition/ subtraction/ multiplication/ division to solve the question.

Complete step-by-step answer:
In this question, we would explain the converting process of radian measures to degrees. The formula for converting radian measures to degrees is shown below,
 \[Degrees = radians \times \dfrac{{{{180}^ \circ }}}{\pi } \to \left( 1 \right)\]
Let’s make an example to understanding the process,
 \[5\pi\; radians \to ?\deg rees\]
In this example we have the radian value, we would convert it into degree value. So, we have,
 \[radians = 5\pi \;radians \to \left( 2 \right)\]
So, the equation \[\left( 1 \right)\] becomes,
 \[\left( 1 \right) \to Degrees = radians \times \dfrac{{{{180}^ \circ }}}{\pi }\]
 \[Degree = 5\pi \times \dfrac{{{{180}^ \circ }}}{\pi }\]
We can cancel the \[\pi \] in the numerator with the \[\pi \] in the denominator. So, we get
 \[
  \deg ree = 5 \times {180^ \circ } \\
  \deg ree = {900^ \circ } \;
 \]
So, we had found that the degree value of \[5\pi \] \[radians\] is \[{900^ \circ }\] . If we convert the degree to radian we can use the following formula,
 \[radians = \deg ree \times \dfrac{\pi }{{{{180}^ \circ }}}\] .
So, the correct answer is “ \[{900^ \circ }\]”.

Note: The radian values are always in terms of \[\pi \] , degree values are always in degree \[\left( {^ \circ } \right)\] . To solve these types of questions we would involve the arithmetic operation of addition/ subtraction/ multiplication/ division to make the easy calculation. Also, remember the formula to convert degree into radian and formula for degree into radian to solve these types of questions. When we convert the radian to degree value, we would cancel the \[\pi \] term. So, we can get the degree value easily. Note that, divided by anything becomes zero, and anything by zero will become zero.