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Math Help - Extrema Trig Functions

  1. #1
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    Extrema Trig Functions

    Find any extrema:

    y = cos(x)-sin(x), XE(-pi, pi)

     dy/dx = -[sin(x)+cos(x)]

    0 = -[sin(x)+cos(x)]

    The problem is not the calculus, it's the solving of this trig equation... Can someone help me please?
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  2. #2
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    Hello, millerst!

    Find any extrema: . y \:=\: \cos x-\sin x,\quad x \in (-\pi, \pi)

     \frac{dy}{dx} \:=\: -\sin x - \cos x \:=\:0

    The problem is not the calculus, it's the solving of this trig equation.
    Can someone help me please?

    We have: . \sin x \:=\:-\cos x

    Divide by \cos x\!:\quad \frac{\sin x}{\cos x} \:=\:-1 \quad\Rightarrow\quad \tan x \:=\:-1 \quad\Rightarrow\quad x \:=\:-\frac{\pi}{4},\;\frac{3\pi}{4}

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