Question

How do you convert 90 degrees to radians?

Answer 1

Hint:
Both the degree and the radians are units of measures of an angle. It is worth remembering that one complete rotation is equal to 360 degrees or 2π radians. How many times 360 is a value of 90? We can multiply both the values by the same number and they will still be equal.

Complete Step by step Solution:
We know that 360 degrees are equal to 2π radians.
If we divide both of them by 4, we will get:
⇒ $ \dfrac{360}{4} $ degrees are equal to $ \dfrac{2\pi }{4} $ radians.

⇒ 90 degrees are equal to $ \dfrac{\pi }{2} $ radians, which is the required answer.

Note:
Angle is a measure of "turn" or "rotation" between two lines. It is measured as a fraction of the complete rotation. If the line reaches the same starting position, it is called a complete rotation.
A degree is the unit of measurement of angles when one complete revolution is divided into 360 equal parts. Each part has measure equal to $ 1{}^\circ $ . The number 360 is chosen because it's easier to do calculations of $ \dfrac{1}{2} $ , $ \dfrac{1}{3} $ , $ \dfrac{1}{5} $ etc. fractions of rotations.
A radian is a unit of measurement of angles where 1 radian is an angle made at the center by an arc of length equal to the radius of the circle. A complete rotation is equal to 2π radians.