How many values of x

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February 23rd 2011, 01:52 AM
hoanghai549

How many values of x

For how many values of http://webwork.math.ttu.edu/wwtmp/eq...dd0b8b8e91.png in the interval

http://webwork.math.ttu.edu/wwtmp/eq...ef23254061.png
is http://webwork.math.ttu.edu/wwtmp/eq...66cd873e31.png?
A. http://webwork.math.ttu.edu/wwtmp/eq...a3da5aab21.png

B. http://webwork.math.ttu.edu/wwtmp/eq...fc95b6a081.png

C. http://webwork.math.ttu.edu/wwtmp/eq...f6db721891.png

D. http://webwork.math.ttu.edu/wwtmp/eq...6774a851b1.png

E. http://webwork.math.ttu.edu/wwtmp/eq...f2f64ba2d1.png
February 23rd 2011, 02:15 AM
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 $\displaystyle \pi \leq x \leq 3\pi$ ?
February 23rd 2011, 02:31 AM
DrSteve

Quote:

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.
February 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.