Question

How to convert 285 degrees to radians?

Answer 1

Hint: We will first mention the value of 1 degree in terms of radians using the unitary method. Then, we will just multiply both sides by 285 and get the required answer.

Complete step by step answer:
We are given that we are required to convert 285 degrees in to radians.
We know that we have: $\pi $ radians equals to 180 degrees.
So, this means that 180 degrees is equal to $\pi $ radians.
Therefore, by using the unitary method, we will get the following equation with us:-
$ \Rightarrow $1 degree is equal to $\dfrac{\pi }{{180}}$ radians.
Now, if we multiply the above equation by 285, we will then obtain the following equation with us:-
$ \Rightarrow $285 degrees is equal to $\dfrac{\pi }{{180}} \times 285$ radians.
If we take out 5 common from both the numerator and denominator and cut them off, we will then obtain the following equation with us:-
$ \Rightarrow $285 degrees is equal to $\dfrac{\pi }{{36}} \times 57$ radians.
Thus, we have 285 degrees as $\dfrac{{57}}{{36}}\pi $ radians.
Now, we can also reduce it in lowest form by cutting off the factor of 3, then we will get:-
285 degrees means $\dfrac{{19}}{{12}}\pi $ radians.

Note: The students must commit to the memory that: $\pi $ radians equals to 180 degrees.
Note that sometimes we require to convert degrees into radians and radians into degrees as well because some formulas require something in a particular unit.
For example:- In the area of the sector of a circle, we may use the value of angle in radians and degrees depending upon the formula we are using for it. Similarly, we can do the same for the arc length of the circle as well.