Pi by 2 (π/2) radians is equal to 90 degrees because of how radians and degrees relate as units for measuring angles. The key is understanding that degrees and radians are just two different units for measuring the same thing: an amount of rotation.
One full circle covers 360 degrees, which is also equal to 2π radians. This relationship can be written as:
Dividing both sides of this equation by 4 leads to:
So, π/2 radians corresponds exactly to 90 degrees because it is one-quarter of the full circle's angle in radians, matching one-quarter of 360 degrees.
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