Q:

# What is 45 degrees in radians?

A:

There are roughly 0.785 radians in 45 degrees, which is the approximation of pi divided by four. It is only an approximation because pi is an irrational number that does not terminate.

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A circle has 360 degrees and 2(pi) radians, and therefore, 180 degrees is equal to pi radians. Using these ratios, the easiest way to convert degrees to radians is to multiply the number of degrees by (pi/180). In the above example, 45 times (pi/180) is equal to (pi/4). The same formula can be used for other common degree calculations. For example, 30 degrees is (pi/6), 60 degrees is (pi/3) and 270 degrees is (3pi/2). To convert the answer to decimal, just replace pi with 3.14. However, in degree/radian calculations, it is customary to just leave pi as is without converting to decimal.

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