Trigonometry Examples

$8 \sin (x) - 4 \csc (x) = 0$

Step 1

Simplify $8 \sin (x) - 4 \csc (x)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Rewrite $\csc (x)$ in terms of sines and cosines.

$8 \sin (x) - 4 \frac{1}{\sin (x)} = 0$

Step 1.1.2

Combine $- 4$ and $\frac{1}{\sin (x)}$ .

$8 \sin (x) + \frac{- 4}{\sin (x)} = 0$

Step 1.1.3

Move the negative in front of the fraction.

$8 \sin (x) - \frac{4}{\sin (x)} = 0$

Step 1.2

Simplify each term.

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Step 1.2.1

Separate fractions.

$8 \sin (x) - (\frac{4}{1} \cdot \frac{1}{\sin (x)}) = 0$

Step 1.2.2

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

$8 \sin (x) - (\frac{4}{1} \csc (x)) = 0$

Step 1.2.3

Divide $4$ by $1$ .

$8 \sin (x) - (4 \csc (x)) = 0$

Step 1.2.4

Multiply $4$ by $- 1$ .

$8 \sin (x) - 4 \csc (x) = 0$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = \frac{π}{4} + \frac{π n}{2}$ , for any integer $n$

Step 3