Question

Need a little help? I am just not getting this, can someone show me based on example ?

Answer 1

I know that \[\sin(A+\frac{π}{2})=\cos(A)\]why can't I say that \[\sin(A+\frac{π}{2})=\sin(A)~~~~~~~~?\]Please example....

Answer 2

If you say that sin(A + pi/2) = cos A and that sin(A + pi/2) = sin A, then that means cos A = sin A? But they aren't quite the same function!

Unless you mean, \( \color{Green}{\cos} (A + \frac{\pi}{2} ) = \sin A \)
In that case, just note that sine and cosine have periods of \(2 \pi\). You can shift sine by pi/2 to get cosine, but shifting by pi/2 again does not make the full period, it is only half. We actually get something close, negative sine of A.

Answer 3

If it helps, imagine rotating the unit circle.