# Extrema Trig Functions

• April 28th 2009, 03:22 PM
millerst
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?
• April 28th 2009, 03:30 PM
Soroban
Hello, millerst!

Quote:

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