Question

Convert $-{\displaystyle \frac{\pi }{6}}$ radians into degrees?

Answer 1

Hint: Radians and degrees are the two measures are units of plane angle. For solving that, we will use the standard form of the radian to degree conversion. The measure of an angle is determined by the amount of rotation from the initial side to the terminal side. In radian, one complete counterclockwise revolution is $2\pi$ and in degree, one complete counterclockwise revolution is ${360}^{\circ }$. So, degree measure and radian measure are related by the equations as below.
${360}^{\circ }=2\pi$ radians and
${180}^{\circ }=\pi$ radians. Here, $\pi$ radians mean a semicircle.

Complete step by step answer:
In this question, we measure angles using the units: degrees and radian.
 As we already know,
${180}^{\circ }=\pi$ radians.
Then the value of 1 degree will be ${\displaystyle \frac{\pi }{180}}$ or we can say that the value of 1 radian is ${\displaystyle \frac{180}{\pi }}$.
The formula to convert radian into degree is:
1 radian=${\displaystyle \frac{180}{\pi }}$degrees.
Therefore, to convert any radian into degree we will multiply the given radian by ${\displaystyle \frac{180}{\pi }}$.
The formula to convert degree into radian is:
Degrees = radians $\times {\displaystyle \frac{{180}^{\circ }}{\pi }}$
In this question, we want to convert $-{\displaystyle \frac{\pi }{6}}$ radians into degrees.
The value of radian into degree will be converted as,
$\Rightarrow -{\displaystyle \frac{\pi }{6}}$ radian $=-{\displaystyle \frac{\pi }{6}}\times {\displaystyle \frac{{180}^{\circ }}{\pi }}$
Let us simplify the right-hand side.
Therefore, we will get:
 $\Rightarrow -{\displaystyle \frac{\pi }{6}}$ radian $=-{30}^{\circ }$
Hence, $-{\displaystyle \frac{\pi }{6}}$ radians is equal to $-{30}^{\circ }$.

Note: To convert degrees to radian, we will multiply the given degree by ${\displaystyle \frac{\pi }{180}}$. We noticed if we have been given two different measurement units whose relation is unknown, So we first convert a single unit to each of them. Then we just divide the two things with which we will get the direct relation of the two units and directly solve.