# Trigonometry Function Help

• May 14th 2011, 02:05 PM
buddah
Trigonometry Function Help
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
• May 14th 2011, 02:12 PM
mr fantastic
Quote:

Originally Posted by buddah
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

Surely your textbook or class notes give you some ideas! What have you tried, where are you stuck?
• May 14th 2011, 02:22 PM
buddah
need help with number 2, just figured out number 1 myself
• May 14th 2011, 04:21 PM
topsquark
Quote:

Originally Posted by buddah
need help with number 2, just figured out number 1 myself

Good! :)

As for number 2, as Mr. Fantastic said, what have you come up with?

-Dan
• May 14th 2011, 04:34 PM
buddah
nothing
• May 14th 2011, 06:03 PM
topsquark
Quote:

Originally Posted by buddah
nothing

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
• May 14th 2011, 06:05 PM
Quacky
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 $\displaystyle \theta$. Let H be the hypotenuse, O the side opposite $\displaystyle \theta$ and A the remaining adjacent side to $\displaystyle \theta$.

Then $\displaystyle Sin~\theta=\frac{O}{H}$ And $\displaystyle Cos~\theta=\frac{A}{H}$.

Remembering that $\displaystyle H^2=A^2+O^2$, it should be easy to show that the identities are valid using Pythagoras.

Edit: beaten by Topsquark