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Solve on the interval [0,2pi): 4cscx+6=-2

Guest Sep 19, 2014

Best Answer 

 #1
avatar+20025 
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Solve on the interval [0,2pi): 4cscx+6=-2

$$\\ 4 \csc{(x)}+6=-2 \quad | \quad -6 \\
4 \csc{(x)}=-8 \quad | \quad :2 \\
\csc{(x)}=-2 \quad | \quad \csc{(x)} = \frac{1}{\sin{(x)}} \\
\frac{1}{ \sin{(x)} } = -2 \\
\sin{(x)} = -\frac{1}{2}$$

$$x_1 = \sin^{-1}{(-\frac{1}{2} )} \\
x_1 = - \sin^{-1}{(\frac{1}{2} )} \\
x_1 = -30 \ensurement{^{\circ}} + 360 \ensurement{^{\circ}} = 330 \ensurement{^{\circ}}$$

$$x_2 = 180 \ensurement{^{\circ}} - (-30 \ensurement{^{\circ}} ) = 210 \ensurement{^{\circ}}$$

heureka  Sep 19, 2014
 #1
avatar+20025 
+8
Best Answer

Solve on the interval [0,2pi): 4cscx+6=-2

$$\\ 4 \csc{(x)}+6=-2 \quad | \quad -6 \\
4 \csc{(x)}=-8 \quad | \quad :2 \\
\csc{(x)}=-2 \quad | \quad \csc{(x)} = \frac{1}{\sin{(x)}} \\
\frac{1}{ \sin{(x)} } = -2 \\
\sin{(x)} = -\frac{1}{2}$$

$$x_1 = \sin^{-1}{(-\frac{1}{2} )} \\
x_1 = - \sin^{-1}{(\frac{1}{2} )} \\
x_1 = -30 \ensurement{^{\circ}} + 360 \ensurement{^{\circ}} = 330 \ensurement{^{\circ}}$$

$$x_2 = 180 \ensurement{^{\circ}} - (-30 \ensurement{^{\circ}} ) = 210 \ensurement{^{\circ}}$$

heureka  Sep 19, 2014

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