It will help you to think in a logical way
When you sing sine, cosine, cosine, tangent
Sine, cosine, tangent, cotangent
Sine, cosine, ..., secant, cosecant
Let's sing a song about trig-functions
sin（2π+α）=sinα
cos（2π+α）=cosα
tan（2π+α）=tanα
which is induction formula1, and induction formula 2
sin（π+α）= —sinα
cos（π+α）=—cosα
tan（π+α）= tanα
sin（π－α）= sinα
cos（π－α）=－cosα
tan（π－α）=－tanα
These are all those "name donot change"
As pi goes to half pi the difference shall be huge
sin（π/2+α）=cosα
sin（π/2－α）=cosα
cos（π/2+α）=－sinα
cos（π/2－α）=sinα
tan（π/2+α）=－cotα