Question

How do you convert \[- \dfrac{\pi}{2}\] to degrees?

Answer 1

Hint: In this question, we need to convert the given radians into degrees. Geometrically, one complete revolution in radians is \[2\pi\]
 and in degrees is \[360^{o}\] . First we need to know the clear definition of radians and degrees. Then by using the formula for the conversion of radians to degrees, we can easily convert the given radians to degrees.
Formula used:
\[1\ \text{radian} = \ \left( \dfrac{180}{\pi} \right)\]

Complete answer:
Definition:
Radians:
The unit of the angle measures is known as radians. The angle made by an arc whose length is equal to the radius of the circle at the centre of a circle is equal to one radian . Mathematically , it is used instead of degrees . We need to know that
\[1\ \text{radian}\ = \ 57.3R\ degrees\]
Degree :
The degree is nothing but a measurement unit of angles. The complete circle is divided into \[360\] degrees. We need to know that One degree is equal \[0.01745329252\] radians.
Now we can convert \[- \dfrac{\pi}{2}\] to degrees,
The formula to convert radians to degree is
\[1\ \text{radian} = \ \left( \dfrac{180}{\pi} \right)^{o}\]
Now we need to convert \[- \dfrac{\pi}{2}\] radians,
\[- \dfrac{\pi}{2}\text{radians}\ = - \dfrac{\pi}{2} \times \left( \dfrac{180}{\pi} \right)^{o}\]
On simplifying,
We get,
\[\Rightarrow \ - \dfrac{180^{o}}{2}\]
On further simplifying,
We get
\[- \dfrac{\pi}{2} = - 90^{o}\]
Thus we have converted \[- \dfrac{\pi}{2}\] to \[-90^{o}\] .
Final answer :
The conversion of \[- \dfrac{\pi}{2}\] to degrees is \[-90^{o}\] .

Note:
Mathematically, Pi (\[\pi\]) is a Greek letter and is a mathematical constant . In trigonometry, the value of is \[180^{o}\] . The degrees are generally used to express both directionality and angle size. Similarly the formula for the conversion of degrees to radians is
\[1\ \text{degree}\ = \dfrac{\pi}{180^{o}}\]
We can check whether our conversion is correct or not by using the formula for the conversion of degrees to radians. The SI unit of the measure of angle is radians. We need to be very careful while writing the units .