Trigonometry Examples

$\frac{52}{\sin (47)} = \frac{x}{\sin (72)}$

Step 1

Subtract $\frac{x}{\sin (72)}$ from both sides of the equation.

$\frac{52}{\sin (47)} - \frac{x}{\sin (72)} = 0$

Step 2

Simplify each term.

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Step 2.1

Separate fractions.

$\frac{52}{1} \cdot \frac{1}{\sin (47)} - \frac{x}{\sin (72)} = 0$

Step 2.2

Convert from $\frac{1}{\sin (47)}$ to $\csc (47)$ .

$\frac{52}{1} \csc (47) - \frac{x}{\sin (72)} = 0$

Step 2.3

Divide $52$ by $1$ .

$52 \csc (47) - \frac{x}{\sin (72)} = 0$

Step 2.4

Evaluate $\csc (47)$ .

$52 \cdot 1.36732746 - \frac{x}{\sin (72)} = 0$

Step 2.5

Multiply $52$ by $1.36732746$ .

$71.10102797 - \frac{x}{\sin (72)} = 0$

Step 2.6

Separate fractions.

$71.10102797 - (\frac{x}{1} \cdot \frac{1}{\sin (72)}) = 0$

Step 2.7

Convert from $\frac{1}{\sin (72)}$ to $\csc (72)$ .

$71.10102797 - (\frac{x}{1} \csc (72)) = 0$

Step 2.8

Divide $x$ by $1$ .

$71.10102797 - (x \csc (72)) = 0$

Step 2.9

Evaluate $\csc (72)$ .

$71.10102797 - (x \cdot 1.05146222) = 0$

Step 2.10

Move $1.05146222$ to the left of $x$ .

$71.10102797 - (1.05146222 \cdot x) = 0$

Step 2.11

Multiply $1.05146222$ by $- 1$ .

$71.10102797 - 1.05146222 x = 0$

Step 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.