How do you graph to solve the equation on the interval $[- 2 π, 2 π]$ $[-2pi,2pi]$ for $csc x = - \frac{2 \sqrt{3}}{3}$ $cscx=-(2sqrt3)/3$ ?

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How do you graph to solve the equation on the interval $[- 2 π, 2 π]$ $[-2pi,2pi]$ for $csc x = - \frac{2 \sqrt{3}}{3}$ $cscx=-(2sqrt3)/3$ ?

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Answer 1 · 2017-02-01T04:47:20

$- \frac{π}{3}, \frac{- 2 π}{3}, \frac{4 π}{3}, \frac{5 π}{3}$ $-pi/3, (-2pi)/3, (4pi)/3, (5pi)/3$

Explanation:

$csc x = \frac{1}{sin x} = - \frac{2 \sqrt{3}}{3}$ $csc x = 1/(sin x) = - (2sqrt3)/3$
$sin x = - \frac{3}{2 \sqrt{3}} = - \frac{\sqrt{3}}{2}$ $sin x = - 3/(2sqrt3) = - sqrt3/2$
Use trig table of special arcs and unit circle:

For interval $(- 2 π, 0)$ $(- 2pi, 0)$ , there are 2 answers:
$sin x = - \frac{\sqrt{3}}{2}$ $sin x = - sqrt3/2$ --> $x = - \frac{π}{3}$ $x = - pi/3$ and $x = \frac{- 2 π}{3}$ $x = (-2pi)/3$
For interval $(0, 2 π)$ $(0, 2pi)$ , there are 2 answers:
sin x = - sqrt3.2 ---> $x = \frac{4 π}{3}$ $x = (4pi)/3$ and $x = \frac{5 π}{3}$ $x = (5pi)/3$

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How do you graph to solve the equation on the interval $[- 2 π, 2 π]$ $[-2pi,2pi]$ for $csc x = - \frac{2 \sqrt{3}}{3}$ $cscx=-(2sqrt3)/3$ ?

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Explanation:

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How do you graph to solve the equation on the interval [−2π,2π][-2pi,2pi] for cscx=−2√33cscx=-(2sqrt3)/3?

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Explanation:

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How do you graph to solve the equation on the interval $[- 2 π, 2 π]$ $[-2pi,2pi]$ for $csc x = - \frac{2 \sqrt{3}}{3}$ $cscx=-(2sqrt3)/3$ ?