Question

How do you convert 75 degrees to radians?

Answer 1

Hint: As we know that the value of an angle in radians is always in the form of $\pi $. So, we will multiply the angle with $\pi $ and at the same time divide it with 180 degrees to equate the numerator and denominator then reduce the fraction to its lowest value.

Complete step by step solution:
As we know that, we need to convert degrees into radians, for this we will multiply the angle with $\dfrac{\pi }{{180^\circ }}$ .
$75^\circ = 75^\circ \times \dfrac{\pi }{{180^\circ }}$
We convert $75^\circ $ and $180^\circ $ into their prime factors and cancel out the similar factors of numerator with denominator.
$ = \dfrac{{5 \times 5 \times 3 \times \pi }}{{3 \times 3 \times 5 \times 2 \times 2}} \Rightarrow \dfrac{{5\pi }}{{12}}$
We multiply the remaining factors and we will get the radian form.H
$ = \dfrac{{5\pi }}{{12}}$

Hence, the value of $75^\circ $ in radians is $\dfrac{{5\pi }}{{12}}$.

Note:
We should remember that the value of $\pi $ is $180^\circ $. So, when we multiply the angle with $\pi $ we always divide the angle by 180 degrees to balance the equation, and to reduce the angle we use the prime factorization method.