# How many values of x

• Feb 23rd 2011, 01:52 AM
hoanghai549
How many values of x
• Feb 23rd 2011, 02:15 AM
Prove It
$\displaystyle \displaystyle \cos{(4x)} = 0$

$\displaystyle \displaystyle 4x = \arccos{(0)}$

$\displaystyle \displaystyle 4x = \frac{\pi}{2} + \pi n$ where $\displaystyle \displaystyle n \in \mathbf{Z}$

$\displaystyle \displaystyle x = \frac{\pi}{8} + \frac{\pi n}{4}$

$\displaystyle \displaystyle x = \frac{\pi + 2\pi n}{8}$.

How many values will lie in the region $\displaystyle \displaystyle \pi \leq x \leq 3\pi$?
• Feb 23rd 2011, 02:31 AM
DrSteve
Quote:

Originally Posted by Prove It
$\displaystyle \displaystyle \cos{(4x)} = 0$

$\displaystyle \displaystyle 4x = \arccos{(0)}$

$\displaystyle \displaystyle 4x = \frac{\pi}{2} + \pi n$ where $\displaystyle \displaystyle n \in \mathbf{Z}$

$\displaystyle \displaystyle x = \frac{\pi}{8} + \frac{\pi n}{4}$

$\displaystyle \displaystyle x = \frac{\pi + 2\pi n}{8}$.

How many values will lie in the region $\displaystyle \displaystyle \pi \leq x \leq 3\pi$?

Technically, the second line should read

$\displaystyle \displaystyle 4x = \arccos{(0)}+ \pi n$ where $\displaystyle \displaystyle n \in \mathbf{Z}$

since $\displaystyle \displaystyle \arccos{x}$ is a function.
• Feb 23rd 2011, 03:22 AM
HallsofIvy
Actually some textbooks use "arccos" (and "arcsin") to include all solutions (so they are NOT functions) and "Arccos" (and "Arcsin") for the functions.