Trigonometry Examples

$b = \frac{\sin (48.9) \cdot 31.3}{\sin (111.4)}$

Step 1

Simplify $\frac{\sin (48.9) \cdot 31.3}{\sin (111.4)}$ .

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Step 1.1

Separate fractions.

$b = \frac{31.3}{1} \cdot \frac{\sin (48.9)}{\sin (111.4)}$

Step 1.2

Rewrite $\frac{\sin (48.9)}{\sin (111.4)}$ as a product.

$b = \frac{31.3}{1} (\sin (48.9) \frac{1}{\sin (111.4)})$

Step 1.3

Write $\sin (48.9)$ as a fraction with denominator $1$ .

$b = \frac{31.3}{1} (\frac{\sin (48.9)}{1} \cdot \frac{1}{\sin (111.4)})$

Step 1.4

Simplify.

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Step 1.4.1

Divide $\sin (48.9)$ by $1$ .

$b = \frac{31.3}{1} (\sin (48.9) \frac{1}{\sin (111.4)})$

Step 1.4.2

Convert from $\frac{1}{\sin (111.4)}$ to $\csc (111.4)$ .

$b = \frac{31.3}{1} (\sin (48.9) \csc (111.4))$

Step 1.5

Divide $31.3$ by $1$ .

$b = 31.3 (\sin (48.9) \csc (111.4))$

Step 1.6

Multiply $31.3 (\sin (48.9) \csc (111.4))$ .

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Step 1.6.1

Multiply $\sin (48.9)$ by $31.3$ .

$b = 23.58653417 \csc (111.4)$

Step 1.6.2

Multiply $23.58653417$ by $\csc (111.4)$ .

$b = 25.33310439$

Step 2

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

$b \approx 30.88958224$

Step 3