Converting Degrees to Radians: A Step-by-Step Guide with Example and Simplification

Converting degrees to radians

To convert degrees to radians, you need to use the conversion formula:

radians = degrees * (π/180)

where π is pi, which is approximately 3

To convert degrees to radians, you need to use the conversion formula:

radians = degrees * (π/180)

where π is pi, which is approximately 3.14159.

Let’s go through an example: convert 45 degrees to radians.

radians = 45 * (π/180)

To simplify the calculation, divide both the numerator and denominator of π/180 by the greatest common divisor (GCD) of 180. In this case, the GCD of 180 is 60.

radians = 45 * (π/60 * 60/180)

Simplifying further, we get:

radians = 45 * (π/60 * 1/3)

radians = 45 * (π/180)

Now substitute the value of π with an approximation of 3.14159:

radians = 45 * (3.14159/180)

radians = 0.7854

Therefore, 45 degrees is approximately 0.7854 radians.

Remember, when converting degrees to radians, always use the conversion formula radians = degrees * (π/180) to ensure accurate conversions.

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