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Math Help - Trigonometry Function Help

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by buddah View Post
    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?
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  3. #3
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    need help with number 2, just figured out number 1 myself
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  4. #4
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    Quote Originally Posted by buddah View Post
    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
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  5. #5
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    nothing
    Last edited by topsquark; May 14th 2011 at 06:02 PM. Reason: Begging
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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by buddah View Post
    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
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  7. #7
    Super Member Quacky's Avatar
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    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 \theta. Let H be the hypotenuse, O the side opposite \theta and A the remaining adjacent side to \theta.

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

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

    Edit: beaten by Topsquark
    Last edited by Quacky; May 15th 2011 at 08:58 AM.
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