Finite Math Examples

$\frac{\sin (a)}{18.9} = \frac{\sin (46.9)}{13.9}$

Step 1

Multiply both sides of the equation by $18.9$ .

$18.9 \frac{\sin (a)}{18.9} = 18.9 \frac{\sin (46.9)}{13.9}$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $18.9$ .

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Step 2.1.1.1

Cancel the common factor.

$18.9 \frac{\sin (a)}{18.9} = 18.9 \frac{\sin (46.9)}{13.9}$

Step 2.1.1.2

Rewrite the expression.

$\sin (a) = 18.9 \frac{\sin (46.9)}{13.9}$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $18.9 \frac{\sin (46.9)}{13.9}$ .

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Step 2.2.1.1

Evaluate $\sin (46.9)$ .

$\sin (a) = 18.9 (\frac{0.73016227}{13.9})$

Step 2.2.1.2

Divide $0.73016227$ by $13.9$ .

$\sin (a) = 18.9 \cdot 0.05252966$

Step 2.2.1.3

Multiply $18.9$ by $0.05252966$ .

$\sin (a) = 0.99281057$

Step 3

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

$a = \arcsin (0.99281057)$

Step 4

Simplify the right side.

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Step 4.1

Evaluate $\arcsin (0.99281057)$ .

$a = 83.12543584$

Step 5

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.

$a = 180 - 83.12543584$

Step 6

Subtract $83.12543584$ from $180$ .

$a = 96.87456415$

Step 7

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

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Step 7.1

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

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

Step 7.2

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

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

Step 7.3

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

$\frac{360}{1}$

Step 7.4

Divide $360$ by $1$ .

$360$

Step 8

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

$a = 83.12543584 + 360 n, 96.87456415 + 360 n$ , for any integer $n$