Extrema Trig Functions

**millerst** · April 28th 2009, 03:22 PM

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?

**Soroban** · April 28th 2009, 03:30 PM

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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