Finding the Half-angle Formula of High School Mathematics (All)

Commonly used half-angle formulas include the following three types:

Half-angle sine formula

Half-angle cosine formula

Half angle tangent formula

The positive and negative values of the trigonometric function are determined by the following formula

Your quadrant determines.

Extended data

Judging from the double-angle formula, there are:

Then, from the relationship between trigonometric functions from the same angle, it is concluded that

geometric proof

In the unit circle, t = tan(φ/2). According to the similarity relation,

It can be concluded that

obviously

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