Question

How do you convert $ {315^ \circ } $ into radians?

Answer 1

Hint: In order to convert $ {315^ \circ } $ into radians, use the concepts of measurement of angles. From these concepts we know that $ {180^ \circ } = \pi $ radians. Take out the value of radian for $ {1^ \circ } $ , then multiply with $ {315^ \circ } $ , and we get our desired results.

Complete step by step solution:
We are given $ {315^ \circ } $ which is in degrees.
From the concepts of measurement of angles we know that $ 180 $ in degrees would be equal to $ \pi $ radians, that is:
 $ {180^ \circ } = \pi $ radians
Need to find the value of radian for $ {1^ \circ } $ , for that divide both sides of the upper equation by $ 180 $ and we get:
 $ {180^ \circ } = \pi $ radians
 $ \dfrac{{{{180}^ \circ }}}{{180}} = \dfrac{\pi }{{180}} $ radians
 $ {1^ \circ } = \dfrac{\pi }{{180}} $ radians
To find the value of $ {315^ \circ } $ , multiply the value of $ 315 $ to the upper equation and we get:
 $ {1^ \circ } \times 315 = 315 \times \dfrac{\pi }{{180}} $ radians
 $ {315^ \circ } = \dfrac{{315\pi }}{{180}} $ radians
We can see that the right-hand side fraction can be simplified.
Since, we know that $ 315 $ and $ 180 $ is both divisible by $ 45 $ . $ 315 $ will be cancelled by $ 45 $ and the remainder it gives will be $ 7 $ whereas $ 180 $ will be cancelled by $ 45 $ and the remainder it gives will be $ 4 $ .And, the simplest form we get is:
 $ {315^ \circ } = \dfrac{{7\pi }}{4} $ radians
Therefore, $ {315^ \circ } $ is equal to $ \dfrac{{7\pi }}{4} $ radians.
So, the correct answer is “ $ \dfrac{{7\pi }}{4} $ radians”.

Note: One radian, written as $ {1^c} $ , is the measure of the angle subtended at the center of a circle by an arc of length equal to the radius of the circle.
Radian is a constant angle.
The vice versa would occur if the question says to convert radian into degree.