Find all values of x in the interval [0, 2π] that satisfy the equation. (Enter your answers as a comma-separated list.)? 18 cos(x) − 9 = 0

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Find all values of x in the interval [0, 2π] that satisfy the equation. (Enter your answers as a comma-separated list.)? 18 cos(x) − 9 = 0

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Answer 1 · 2018-01-15T02:29:42

$x = \frac{π}{3}, \frac{5 π}{3}$ $x=pi/3, (5pi)/3$

Explanation:

First isolate X:
$18 cos x - 9 = 0$ $18cosx-9=0$
$18 cos x = 9$ $18cosx=9$
$cos x = \frac{9}{18}$ $cosx=9/18$
$cos x = \frac{1}{2}$ $cosx=1/2$
Now that we know that Cosine of X = $\frac{1}{2}$ $1/2$ , we can use the unit circle to find which angles satisty the equation.
Points on the unit circle are $(cos, sin)$ $(cos, sin)$ , so any point on the unit circle that has an x value of $\frac{1}{2}$ $1/2$ is a solution. The angles that satisfy this condition are $\frac{π}{3}$ $pi/3$ and $\frac{5 π}{3}$ $(5pi)/3$ .

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Find all values of x in the interval [0, 2π] that satisfy the equation. (Enter your answers as a comma-separated list.)? 18 cos(x) − 9 = 0

1 Answer

Explanation:

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