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Math Help - Absolute extreme values of sin and cos

  1. #1
    Newbie darkfenix21's Avatar
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    Absolute extreme values of sin and cos

    Hi there just wondering if someone could answer a question I have.
    I've been given the function:

    f(x)= cos x + sin x with a domain of [0,π] π <--- is pi (3.14)

    and it wants me to determine the coordinates of the point where the tangent is horizontal.

    I know first off I must take the derivative of this and I get

    f ' (x)= cos x - sin x (i've just rearanged so the negative isn't infront)

    0=cos x - sin x (set to zero)

    sin x = cos x move sin over to make it equal

    (sin x = cos x) / cos x divide both sides by cos

    tan x = 1 this gives us the idenity (sinx/cosx =tanx) and 1


    **this is where I get stuck I don't understand where I go from here to determine the coordinates if someone could show me it be much appreciated. Thank you
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  2. #2
    MHF Contributor
    skeeter's Avatar
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    Quote Originally Posted by darkfenix21 View Post
    Hi there just wondering if someone could answer a question I have.
    I've been given the function:

    f(x)= cos x + sin x with a domain of [0,π] π <--- is pi (3.14)

    and it wants me to determine the coordinates of the point where the tangent is horizontal.

    I know first off I must take the derivative of this and I get

    f ' (x)= cos x - sin x (i've just rearanged so the negative isn't infront)

    0=cos x - sin x (set to zero)

    sin x = cos x move sin over to make it equal

    (sin x = cos x) / cos x divide both sides by cos

    tan x = 1 this gives us the idenity (sinx/cosx =tanx) and 1


    **this is where I get stuck I don't understand where I go from here to determine the coordinates if someone could show me it be much appreciated. Thank you
    from the unit circle ...

     <br />
\sin{x} = \cos{x} at x = \frac{\pi}{4} + k\pi \, ; \, k \in \mathbb{Z}<br />
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  3. #3
    Newbie darkfenix21's Avatar
    Joined
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    Ahh that makes much more sense to me. I guess I went to far ahead with simplifying it for my own good.
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