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
Okay, I can't post a picture of this, so I'll have to describe it. Consider a right triangle with a hypotenuse of length 1. Put one of the angles of the triangle to be (theta). What are the two other sides of the triangle equal to? What does the Pythagorean theorem say?
-Dan
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