Question

What‌ ‌is‌ ‌$-\dfrac{3\pi‌ ‌}{2}$‌ ‌radians‌ ‌in‌ ‌degrees?‌ ‌

Answer 1

Hint: We know that ${{\pi }^{c}}=180{}^\circ .$ So, if we transpose $\pi $ to the right-hand side, we will get ${{\left( \dfrac{180}{\pi } \right)}^{\circ }}={{1}^{c}}.$ So, we need to multiply a value in radian with $\left( \dfrac{180}{\pi} \right)$ to get the value in degrees.

Complete step-by-step solution:
Let us consider the given problem.
We are asked to find the value of $-{{\dfrac{3\pi }{2}}^{c}}$ in degrees.
We know that ${{\pi }^{c}}=180{}^\circ .$
Now, we need to transpose $\pi $ from the left-hand side to the right-hand side.
We will get ${{1}^{c}}={{\left( \dfrac{180}{\pi } \right)}^{\circ }}.$
So, we will learn that ${{1}^{c}}$ is equal to ${{\left( \dfrac{180}{\pi } \right)}^{\circ }}.$
So, to convert a value in radian to a value in degree, we need to multiply the radian value with ${{\left( \dfrac{180}{\pi } \right)}^{\circ }}$
That is, if we want to convert $-{{\dfrac{3\pi }{2}}^{c}}$ to degree, we need to multiply it with ${{\left( \dfrac{180}{\pi } \right)}^{\circ }}.$
So, we will get $-\dfrac{3\pi }{2}{{\left( \dfrac{180}{\pi } \right)}^{\circ }}.$
And so, we will cancel $\pi $ from both the numerator and the denominator.
Then, we will get $-\dfrac{3}{2}{{\left( \dfrac{180}{1} \right)}^{\circ }}.$
As we know, $2$ is a common factor in the numerator and the denominator. So, we will cancel that off.
So, as a result of this cancellation, we will get $-3\times 90=-270{}^\circ .$
Since the sign is negative, we conclude that the angle is measured in the clockwise direction.
In that case, we need to subtract $270$ from $360$ so that we will be able to find out the angle measured in the anticlockwise direction.
And so, we will get $360-270=90.$
So, we will get $-270{}^\circ =90{}^\circ .$
Hence the value of $-\dfrac{3\pi }{2}$ radians in degrees is obtained as $90{}^\circ .$

Note: We know that we can convert the angle measurements from radians to degrees and from degrees to radians by using the identity ${{\pi }^{c}}=180{}^\circ .$ To convert from radians to degrees, we need to multiply the given value with ${{\left( \dfrac{180}{\pi } \right)}^{\circ }}$ and to convert from degrees to radians, we need to multiply the given value with ${{\left( \dfrac{\pi }{180} \right)}^{c}}.$