Question

Express in radian the following angle:
(a)$395{}^\circ$
(b)$60{}^\circ$

Answer 1

Hint: We will use the formula $\text{Angle in radian}=\dfrac{\pi }{180}\times \text{Angle in degree}$ , to convert degree into radian and then we will substitute the value of degree in the formula that is given in the question to find the value in radian and that will be the final answer.

Complete step-by-step answer:
Let’s start our solution by first writing the relation between degree to minutes and seconds.
Let’s first solve part (a),
For (a):
Now we have $395{}^\circ$,
Now we will use the formula that helps us to convert degree into radian.
The formula that converts degree into radian is:
$\text{Angle in radian}=\dfrac{\pi }{180}\times \text{Angle in degree}$
Now substituting the value of degree as 395 in the above formula we get,
$\begin{aligned} & \text{Angle in radian}=\dfrac{\pi }{180}\times 395 \\\ & \text{Angle in radian}=\dfrac{79\pi }{36} \\\ \end{aligned}$
Hence, the answer for (a) is $\dfrac{79\pi }{36}$ .
For (b):
Now we have$60{}^\circ$ ,
Now we will use the formula that helps us to convert degree into radian.
The formula that converts degree into radian is:
$\text{Angle in radian}=\dfrac{\pi }{180}\times \text{Angle in degree}$
Now substituting the value of degree as 60 in the above formula we get,
$\begin{aligned} & \text{Angle in radian}=\dfrac{\pi }{180}\times 60 \\\ & \text{Angle in radian}=\dfrac{\pi }{3} \\\ \end{aligned}$
Hence, the answer for (b) is $\dfrac{\pi }{3}$ .

Note: The formula that we have used for conversion is$\text{Angle in radian}=\dfrac{\pi }{180}\times \text{Angle in degree}$ and the minute of arc method must be kept in mind. And this formula must be kept in mind. From this formula we can also find the value of angle in degree if the value of angle in radian is given. So, in some questions the value of angle in radian might be given and we need to find the value of angle in degree, then also we will use the same formula for the purpose.