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.