Precalculus Examples

$\frac{\sin (137)}{14} = \frac{\sin (c)}{9}$

Step 1

Rewrite the equation as $\frac{\sin (c)}{9} = \frac{\sin (137)}{14}$ .

$\frac{\sin (c)}{9} = \frac{\sin (137)}{14}$

Step 2

Multiply both sides of the equation by $9$ .

$9 \frac{\sin (c)}{9} = 9 \frac{\sin (137)}{14}$

Step 3

Simplify both sides of the equation.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Cancel the common factor of $9$ .

Tap for more steps...

Step 3.1.1.1

Cancel the common factor.

$9 \frac{\sin (c)}{9} = 9 \frac{\sin (137)}{14}$

Step 3.1.1.2

Rewrite the expression.

$\sin (c) = 9 \frac{\sin (137)}{14}$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Simplify $9 \frac{\sin (137)}{14}$ .

Tap for more steps...

Step 3.2.1.1

Evaluate $\sin (137)$ .

$\sin (c) = 9 (\frac{0.68199836}{14})$

Step 3.2.1.2

Divide $0.68199836$ by $14$ .

$\sin (c) = 9 \cdot 0.04871416$

Step 3.2.1.3

Multiply $9$ by $0.04871416$ .

$\sin (c) = 0.43842751$

Step 4

Take the inverse sine of both sides of the equation to extract $c$ from inside the sine.

$c = \arcsin (0.43842751)$

Step 5

Simplify the right side.

Tap for more steps...

Step 5.1

Evaluate $\arcsin (0.43842751)$ .

$c = 26.00359352$

Step 6

The sine function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from $180$ to find the solution in the second quadrant.

$c = 180 - 26.00359352$

Step 7

Subtract $26.00359352$ from $180$ .

$c = 153.99640647$

Step 8

Find the period of $\sin (c)$ .

Tap for more steps...

Step 8.1

The period of the function can be calculated using $\frac{360}{| b |}$ .

$\frac{360}{| b |}$

Step 8.2

Replace $b$ with $1$ in the formula for period.

$\frac{360}{| 1 |}$

Step 8.3

The absolute value is the distance between a number and zero. The distance between $0$ and $1$ is $1$ .

$\frac{360}{1}$

Step 8.4

Divide $360$ by $1$ .

$360$

Step 9

The period of the $\sin (c)$ function is $360$ so values will repeat every $360$ degrees in both directions.

$c = 26.00359352 + 360 n, 153.99640647 + 360 n$ , for any integer $n$