1. Explain why the functions y= cos x and y = sin(x+90) are the same function. Explanation must be detailed include graphs if you wish.
2. Outline why the identities are referred to as Pythagorean identities:
sinēθ + cosēθ = 1
1 + tanēθ = secēθ
1 + cotēθ = csc ēθ
Because they can quite easily be derived using Pythagoras' theorem? I assume that's what you're being asked to show.
Well, construct yourself a right-angled triangle, with an unknown angle . Let H be the hypotenuse, O the side opposite and A the remaining adjacent side to .
Then And .
Remembering that , it should be easy to show that the identities are valid using Pythagoras.
Edit: beaten by Topsquark