Question

How do you convert \[\dfrac{\pi }{8}\] radians in degrees?

Answer 1

Hint: There are two units of measure for an angle. One is called degree (denoted by \[{}^\circ \] sign). And the other unit of measure is radian, radian is denoted by rad but it is not denoted by using this notation generally. Every angle can either be measured in degree or radian. The measure of angles can also be converted from one unit to another unit.
The conversion formula is as follows: From radian to degree – measure of angle in radian \[\times \dfrac{180{}^\circ }{\pi }\]. After substituting it, we need to cancel the common factors from numerators and denominators to get the simplest form.

Complete step by step solution:
We are asked to convert \[\dfrac{\pi }{8}\] to degrees. To do this we will use the formula for radian to degree conversion. This formula is expressed as from radian to degree – measure of angle in radian \[\times \dfrac{180{}^\circ }{\pi }\].
Substituting the value of angle as \[\dfrac{\pi }{8}\] in the above formula, we get \[\dfrac{\pi }{8}\times \dfrac{180{}^\circ }{\pi }\]. The numerator and denominator have a common factor, also we can divide 180 by 8 to get a decimal answer. Cancelling out the common factors from the numerator and denominator we get simplified form as \[{{22.5}^{\circ }}\].
Thus, we get 22.5 degrees as required.

Note:This conversion formula is very important as we will need in many types of questions like questions of trigonometry, co-ordinate geometry etc.
We should also remember the inverse of this that is, conversion formula from radian to degree, this formula is expressed as follows:
From degree to radian – measure of angle in degree \[\times \dfrac{\pi }{180{}^\circ }\] .