# Math Help - Conditional Trigonomettric Equations help need

1. ## Conditional Trigonomettric Equations help need

Solve the equation for exact solutions over the interval 0,2π

(cscx + 2)(cscx - squareroot2) = 0

2. Hello, nee!

The problem is 90% solved for you already.

Solve the equation for exact solutions over the interval $[0,2\pi]$

$(\csc x + 2)(\csc x - \sqrt{2}) \:= \:0$

Set each factor equal to zero and solve . . .

$\csc x + 2 \:=\:0 \quad\Rightarrow\quad \csc x \:=\:-2\quad\Rightarrow\quad x \:=\:\frac{7\pi}{6},\;\frac{11\pi}{6}$

$\csc x - \sqrt{2}\:=\:0 \quad\Rightarrow\quad \csc x \:=\:\sqrt{2}\quad\Rightarrow\quad x \:=\:\frac{\pi}{4},\;\frac{3\pi}{4}$

3. set each factor equal to zero. solutions are right off the unit circle, which you have memorized, right?

$\csc{x} = -2$

$\sin{x} = -\frac{1}{2}$

$x = \frac{7\pi}{6}$ , $x = \frac{11\pi}{6}$

$\csc{x} = \sqrt{2}$

$\sin{x} = \frac{1}{\sqrt{2}}$

$x = \frac{\pi}{4}$ , $x = \frac{3\pi}{4}$

Soroban getting too fast in my old age.

4. Ok took me a few but I think I got it. Thanks for your help! NEE!!!