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Half Angle Identities


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👉 Proof of Half Angle Identities

Half Angle Identities calculator computes the half angle for sin (u/2), cos (u/2) and tan (u/2) for given angle using basic formulas:
sin(u/2) = + or - √ (1 – cos u) / 2.
cos(u/2) = + or - √ (1 + cos u) / 2.
The half-angle formulas allow the expression of trigonometric functions to determine the trigonometric values for another angle u/2 in terms of u. The half-angle formulas are useful in finding the values of unknown trigonometric functions. The half-angle formulas for any angle u can be stated as follows:
sin(u/2) = + or - √ (1 – cos u) / 2.
In the case of u is in first and second quadrant then function is positive and in the case of u is in third and forth quadrant then function is negative.
cos(u/2) = + or - √ (1 + cos u) / 2.
In the case of u is in first and forth quadrant then function is positive and in the case of u is in second and third quadrant then function is negative.