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".