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What is the definition of trigonometric function with four acute angles required in senior high school mathematics? Ask for a detailed explanation! ! Later inductive formulas cannot be used.
As I am a high school student, I can't understand trigonometric functions only in right triangles, but in coordinate axes.

Let A(x,

y),x^2+y^2=r^2

sinα=y/r

cosα=x/r

tanα=y/x

So we can understand the symbols of trigonometric functions on each coordinate axis.

There are positive, negative and positive sins.

Cos is positive, negative and positive.

Tan is affirmative and negative.

As for sin(α+π/2) and sin(α+π/4), the result is "parity unchanged, sign according to quadrant".