Question

How do you convert $25$ degrees to radians?

Answer 1

Hint: Start by multiplying the term by $\dfrac{\pi }{{180}}$ . Then reduce the terms until it cannot be reduced any further. Cancel any common factors if possible. Finally convert the term into decimal. Make sure the terms are not in fractional form.

Complete step-by-step answer:
First we will start off by converting radians to degrees by multiplying $\dfrac{\pi }{{180}}$ to the term $25$. Since, a full circle is ${360^0}$ or $2\pi $ radians.
 \[\left( {25} \right) \times \left( {\dfrac{\pi }{{180}}} \right)\]
Now we will cancel the common factor if possible.
 \[\left( {25} \right) \times \left( {\dfrac{\pi }{{180}}} \right)\]
Now we cancel the common factor of $5$.
 \[\left( 5 \right) \times \left( {\dfrac{\pi }{{36}}} \right)\]
Hence, the angle $25$ in radians is \[\dfrac{{5\pi }}{{36}}\] .
So, the correct answer is \[\dfrac{{5\pi }}{{36}}\] ”.

Note: The measure of an angle is determined by the amount of rotation from the initial side to the terminal side. A radian is a measure of an angle that, when drawn as a central angle of a circle, intercepts an arc whose length is equal to the length of the radius of the circle. The general formula for converting an angle from degrees to radians is to simply multiply the number of degrees by $\dfrac{\pi }{{180}}$ and the general formula for converting from radians to degrees to simply multiply the number of degrees by $\dfrac{{180}}{\pi }$.