Answer:
See proof and explanation below.
Step-by-step explanation:
First we can proof this analitically first using the following property:
[tex] sin(a+b) = sin(a) cos(b) + sin (b) cos(a)[/tex]
If we apply this into our formula we got:
[tex] sin (x + \frac{\pi}{2}) = sin (x) cos(\frac{\pi}{2}) + sin (\frac{\pi}{2}) cos (x) [/tex]
And if we simplify we got:
[tex] sin (x + \frac{\pi}{2}) = sin (\frac{\pi}{2}) cos (x)= cos (x)[/tex]
And that complete the proof.
If we analyze the graphs sin(x) and cos (x) we see that we have a gap between two graphs of [tex]\pi/2[/tex] as we can see on the figure attached.
When we do the transformation [tex] sin(x +\pi/2) [/tex] we are moving to the left [tex]\pi/2[/tex] units and then would be exactly the cos function.
