# How do you solve y = 2 cos 3 (x - (pi/4))?

Apr 27, 2015

Solve $y = 2. \cos 3 \left(x - \frac{\Pi}{4}\right) = 0$.

Call $\left(x - \frac{\Pi}{4}\right) = t \to y = 2. \cos 3 t = 0$

cos 3t = 0 --> 3t = Pi/2; and 3t = 3Pi/2

$3 t = \frac{\Pi}{2} \to t = \frac{\Pi}{6} \left(1\right)$

$3 t = 3 \frac{\Pi}{2} \to t = \frac{\Pi}{2} \left(2\right)$

$\left(1\right) t = \left(x - \frac{\Pi}{4}\right) = \frac{\Pi}{6} \to x = 5 \frac{\Pi}{12}$

$\left(2\right) t = \left(x - \frac{\Pi}{4}\right) = \frac{\Pi}{2} \to x = \frac{\Pi}{2} + \frac{\pi}{4} = 6 \frac{\Pi}{8} = 3 \frac{\Pi}{4}$

$x = 5 \frac{\Pi}{12} \mathmr{and} x = 3 \frac{\Pi}{4}$

Check:

(1) $x = 5 \frac{\Pi}{12} \to t = x - \frac{\Pi}{4} = 5 \frac{\Pi}{12} - \frac{\Pi}{4} = \frac{\Pi}{6} \to 3 t = 3 \frac{\Pi}{6} = \frac{\Pi}{2} \to \cos 3 t = \cos \frac{\Pi}{2} = 0$.

Correct.

(2) $x = 3 \frac{\Pi}{4} \to t = \left(x - \frac{\Pi}{4}\right) = 3 \frac{\Pi}{4} - \frac{\Pi}{4} = \frac{\Pi}{2} \to 3 t = 3 \frac{\Pi}{2} \to \cos 3 t = \cos 3 \frac{\Pi}{2} = 0$.

Correct.