# Thread: How many values of x

1. ## How many values of x

For how many values of in the interval
is ?
A.

B.

C.

D.

E.

2. $\displaystyle \cos{(4x)} = 0$

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

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

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

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

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

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

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

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

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

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

How many values will lie in the region $\displaystyle \pi \leq x \leq 3\pi$?
Technically, the second line should read

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

since $\displaystyle \arccos{x}$ is a function.

4. Actually some textbooks use "arccos" (and "arcsin") to include all solutions (so they are NOT functions) and "Arccos" (and "Arcsin") for the functions.