Question Video: Converting Degrees to Radians Mathematics • First Year of Secondary School

Video Transcript

True or false: The correct formula to convert 50 degrees to radians is 50 degrees times 𝜋 over 180 degrees.

In this question, we’re asked exactly how we convert an angle in degrees to one in radians. A useful conversion that we can recall and use here is that 180 degrees is equal to 𝜋 radians. We could then use this conversion to work out what one degree would be in radians. Dividing both sides of the conversion by 180 would give us that one degree is equal to 𝜋 over 180 radians. We could then find 50 degrees in radians by multiplying 𝜋 over 180 by 50. This is the same method employed in the statement in the question. And so we can say that this is a true statement.

We answered this question by applying this common conversion. However, we could have also used the fact that to convert an angle in degrees to one in radians, we multiply the given angle by 𝜋 over 180. Although we weren’t asked to work out 50 degrees in radians, we could give it as five eighteenths 𝜋 radians or as a decimal approximation of 0.87 radians.