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Question: What‌ ‌is‌ ‌\(-\dfrac{3\pi‌ ‌}{2}\)‌ ‌radians‌ ‌in‌ ‌degrees?‌ ‌...

What‌ ‌is‌ ‌−3π‌‌2-\dfrac{3\pi‌ ‌}{2}‌ ‌radians‌ ‌in‌ ‌degrees?‌ ‌

Explanation

Solution

We know that πc=180∘.{{\pi }^{c}}=180{}^\circ . So, if we transpose π\pi to the right-hand side, we will get (180π)∘=1c.{{\left( \dfrac{180}{\pi } \right)}^{\circ }}={{1}^{c}}. So, we need to multiply a value in radian with (180π)\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 −3π2c-{{\dfrac{3\pi }{2}}^{c}} in degrees.
We know that πc=180∘.{{\pi }^{c}}=180{}^\circ .
Now, we need to transpose π\pi from the left-hand side to the right-hand side.
We will get 1c=(180π)∘.{{1}^{c}}={{\left( \dfrac{180}{\pi } \right)}^{\circ }}.
So, we will learn that 1c{{1}^{c}} is equal to (180π)∘.{{\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 (180π)∘{{\left( \dfrac{180}{\pi } \right)}^{\circ }}
That is, if we want to convert −3π2c-{{\dfrac{3\pi }{2}}^{c}} to degree, we need to multiply it with (180π)∘.{{\left( \dfrac{180}{\pi } \right)}^{\circ }}.
So, we will get −3π2(180π)∘.-\dfrac{3\pi }{2}{{\left( \dfrac{180}{\pi } \right)}^{\circ }}.
And so, we will cancel π\pi from both the numerator and the denominator.
Then, we will get −32(1801)∘.-\dfrac{3}{2}{{\left( \dfrac{180}{1} \right)}^{\circ }}.
As we know, 22 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 −3×90=−270∘.-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 270270 from 360360 so that we will be able to find out the angle measured in the anticlockwise direction.
And so, we will get 360−270=90.360-270=90.
So, we will get −270∘=90∘.-270{}^\circ =90{}^\circ .
Hence the value of −3π2-\dfrac{3\pi }{2} radians in degrees is obtained as 90∘.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 πc=180∘.{{\pi }^{c}}=180{}^\circ . To convert from radians to degrees, we need to multiply the given value with (180π)∘{{\left( \dfrac{180}{\pi } \right)}^{\circ }} and to convert from degrees to radians, we need to multiply the given value with (π180)c.{{\left( \dfrac{\pi }{180} \right)}^{c}}.