When I enter cos(45) into a calculator, what calculations are being made?
And don't say 1/sec(x) or equivalent trig. identities.
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Create (or imagine) a right triangle whose legs are of length = 1, then the hypotenuse is sqrt(2). the angles (other than the right angle) are 45 degrees, Then pick on of the 45 degree angles, and then TAN 45(degrees) = 1/1 = 1. SIN 45(degrees) = 1/sqrt(2). COS 45(degrees) = 1/sqrt(2). These are the exact ratios.