Precalculus Examples

$\frac{\sin (98.4)}{10.6782} = \frac{\sin (y)}{8}$

Step 1

Rewrite the equation as $\frac{\sin (y)}{8} = \frac{\sin (98.4)}{10.6782}$ .

$\frac{\sin (y)}{8} = \frac{\sin (98.4)}{10.6782}$

Step 2

Multiply both sides of the equation by $8$ .

$8 \frac{\sin (y)}{8} = 8 \frac{\sin (98.4)}{10.6782}$

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 $8$ .

Tap for more steps...

Step 3.1.1.1

Cancel the common factor.

$8 \frac{\sin (y)}{8} = 8 \frac{\sin (98.4)}{10.6782}$

Step 3.1.1.2

Rewrite the expression.

$\sin (y) = 8 \frac{\sin (98.4)}{10.6782}$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Simplify $8 \frac{\sin (98.4)}{10.6782}$ .

Tap for more steps...

Step 3.2.1.1

Evaluate $\sin (98.4)$ .

$\sin (y) = 8 (\frac{0.98927233}{10.6782})$

Step 3.2.1.2

Divide $0.98927233$ by $10.6782$ .

$\sin (y) = 8 \cdot 0.0926441$

Step 3.2.1.3

Multiply $8$ by $0.0926441$ .

$\sin (y) = 0.74115287$

Step 4

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

$y = \arcsin (0.74115287)$

Step 5

Simplify the right side.

Tap for more steps...

Step 5.1

Evaluate $\arcsin (0.74115287)$ .

$y = 47.82971591$

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.

$y = 180 - 47.82971591$

Step 7

Subtract $47.82971591$ from $180$ .

$y = 132.17028408$

Step 8

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

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 $\sin (y)$ function is $360$ so values will repeat every $360$ degrees in both directions.

$y = 47.82971591 + 360 n, 132.17028408 + 360 n$ , for any integer $n$