Question

How do you convert $- 40$ degrees into radians?

Answer 1

Hint : Degree and radians are two separate units which are used as units for the measurement of angles. A degree is a unit to measure angle. A degree is usually denoted as $^ \circ$ . One degree is equal to $\dfrac{\pi }{{180}}$ radians which approximately equals to $0.01746$ radians. In order to convert any given angle from a measure of its degrees to radian, we have to multiply the value by $\dfrac{\pi }{{180}}$ . A radian is the angle made at the center of the circle by an arc equal in length to the radius. One radian equals to $\dfrac{{180}}{\pi }$ degrees which approximately equals to ${57^ \circ }16'$ . In order to convert any given angle from the measure of its radians to degrees, all we are needed to do is multiply the value by $\dfrac{{180}}{\pi }$ .

Complete step-by-step answer :
We know that a circle subtends at the center an angle whose radian measure is $2\pi$ whereas its degree measure is $360$ , it follows that
$2\pi \;radian = {360^ \circ } \\\ \pi \;radian = {180^ \circ } \;$
In order to convert a degree into radian, we need to multiply the given degree by $\dfrac{\pi }{{180}}$ .
$\Rightarrow - {40^ \circ } \times \dfrac{\pi }{{{{180}^ \circ }}} \\\ \Rightarrow - 0.22222\pi \;rad \\\ \Rightarrow - 0.698\;rad \;$
So, the correct answer is “ 0.698 RAD”.

Note : To convert degree into radian we are required to multiply the degree by $\dfrac{\pi }{{180}}$ . This is usually confused by students with $\dfrac{{180}}{\pi }$ which is the formula used when we are required to convert radians into degrees. A circle has ${360^ \circ }$ degree or $2\pi$ radians. Radians have useful properties in calculus under this we define trigonometric functions with radians as its units they can easily be derived while degrees don’t have such useful properties but helps in divisibility.