Basic Math Examples

\frac{14}{sin (B)} = \frac{9}{sin (35)}

$\frac{14}{\sin (B)} = \frac{9}{\sin (35)}$

Step 1

Factor each term.

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Step 1.1

Separate fractions.

\frac{14}{sin (B)} = \frac{9}{1} \cdot \frac{1}{sin (35)}

$\frac{14}{\sin (B)} = \frac{9}{1} \cdot \frac{1}{\sin (35)}$

Step 1.2

Convert from

\frac{1}{sin (35)}

$\frac{1}{\sin (35)}$ to

csc (35)

$\csc (35)$ .

\frac{14}{sin (B)} = \frac{9}{1} csc (35)

$\frac{14}{\sin (B)} = \frac{9}{1} \csc (35)$

Step 1.3

Divide

9

$9$ by

1

$1$ .

\frac{14}{sin (B)} = 9 csc (35)

$\frac{14}{\sin (B)} = 9 \csc (35)$

Step 1.4

Evaluate

csc (35)

$\csc (35)$ .

\frac{14}{sin (B)} = 9 \cdot 1.74344679

$\frac{14}{\sin (B)} = 9 \cdot 1.74344679$

Step 1.5

Multiply

9

$9$ by

1.74344679

$1.74344679$ .

\frac{14}{sin (B)} = 15.69102116

$\frac{14}{\sin (B)} = 15.69102116$

\frac{14}{sin (B)} = 15.69102116

$\frac{14}{\sin (B)} = 15.69102116$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

sin (B), 1

$\sin (B), 1$

Step 2.2

The LCM of one and any expression is the expression.

sin (B)

$\sin (B)$

sin (B)

$\sin (B)$

Step 3

Multiply each term in

\frac{14}{sin (B)} = 15.69102116

$\frac{14}{\sin (B)} = 15.69102116$ by

sin (B)

$\sin (B)$ to eliminate the fractions.

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Step 3.1

Multiply each term in

\frac{14}{sin (B)} = 15.69102116

$\frac{14}{\sin (B)} = 15.69102116$ by

sin (B)

$\sin (B)$ .

\frac{14}{sin (B)} sin (B) = 15.69102116 sin (B)

$\frac{14}{\sin (B)} \sin (B) = 15.69102116 \sin (B)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of

sin (B)

$\sin (B)$ .

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Step 3.2.1.1

Cancel the common factor.

\frac{14}{sin (B)} sin (B) = 15.69102116 sin (B)

$\frac{14}{\sin (B)} \sin (B) = 15.69102116 \sin (B)$

Step 3.2.1.2

Rewrite the expression.

14 = 15.69102116 sin (B)

$14 = 15.69102116 \sin (B)$

14 = 15.69102116 sin (B)

$14 = 15.69102116 \sin (B)$

14 = 15.69102116 sin (B)

$14 = 15.69102116 \sin (B)$

14 = 15.69102116 sin (B)

$14 = 15.69102116 \sin (B)$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as

15.69102116 sin (B) = 14

$15.69102116 \sin (B) = 14$ .

15.69102116 sin (B) = 14

$15.69102116 \sin (B) = 14$

Step 4.2

Divide each term in

15.69102116 sin (B) = 14

$15.69102116 \sin (B) = 14$ by

15.69102116

$15.69102116$ and simplify.

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Step 4.2.1

Divide each term in

15.69102116 sin (B) = 14

$15.69102116 \sin (B) = 14$ by

15.69102116

$15.69102116$ .

\frac{15.69102116 sin (B)}{15.69102116} = \frac{14}{15.69102116}

$\frac{15.69102116 \sin (B)}{15.69102116} = \frac{14}{15.69102116}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of

15.69102116

$15.69102116$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{15.69102116 \sin (B)}{15.69102116} = \frac{14}{15.69102116}$

Step 4.2.2.1.2

Divide

$\sin (B)$ by

$1$ .

$\sin (B) = \frac{14}{15.69102116}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide

$14$ by

$15.69102116$ .

$\sin (B) = 0.89223001$

Step 5

Take the inverse sine of both sides of the equation to extract

$B$ from inside the sine.

$B = \arcsin (0.89223001)$

Step 6

Simplify the right side.

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Step 6.1

Evaluate

$\arcsin (0.89223001)$ .

$B = 63.15482075$

Step 7

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.

$B = 180 - 63.15482075$

Step 8

Subtract

$63.15482075$ from

$180$ .

$B = 116.84517924$

Step 9

Find the period of

$\sin (B)$ .

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Step 9.1

The period of the function can be calculated using

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

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

Step 9.2

Replace

$b$ with

$1$ in the formula for period.

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

Step 9.3

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

$0$ and

$1$ is

$1$ .

$\frac{360}{1}$

Step 9.4

Divide

$360$ by

$1$ .

$360$

Step 10

The period of the

$\sin (B)$ function is

$360$ so values will repeat every

$360$ degrees in both directions.

$B = 63.15482075 + 360 n, 116.84517924 + 360 n$ , for any integer

$n$