Trigonometry Examples

$\frac{\sin (30)}{10} = \frac{\sin (40)}{x}$

Step 1

Simplify $\frac{\sin (30)}{10}$ .

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Step 1.1

The exact value of $\sin (30)$ is $\frac{1}{2}$ .

$\frac{\frac{1}{2}}{10} = \frac{\sin (40)}{x}$

Step 1.2

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{2} \cdot \frac{1}{10} = \frac{\sin (40)}{x}$

Step 1.3

Multiply $\frac{1}{2} \cdot \frac{1}{10}$ .

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Step 1.3.1

Multiply $\frac{1}{2}$ by $\frac{1}{10}$ .

$\frac{1}{2 \cdot 10} = \frac{\sin (40)}{x}$

Step 1.3.2

Multiply $2$ by $10$ .

$\frac{1}{20} = \frac{\sin (40)}{x}$

Step 2

Evaluate $\sin (40)$ .

$\frac{1}{20} = \frac{0.6427876}{x}$

Step 3

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

$x \approx - 7.54138984$

Step 4