Basic Math Examples

sin (x) = 90.4 \cdot 9.8 \div 4820

$\sin (x) = 90.4 \cdot 9.8 \div 4820$

Step 1

Simplify

90.4 \cdot 9.8 \div 4820

$90.4 \cdot 9.8 \div 4820$ .

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Step 1.1

Rewrite the division as a fraction.

sin (x) = \frac{90.4 \cdot 9.8}{4820}

$\sin (x) = \frac{90.4 \cdot 9.8}{4820}$

Step 1.2

Multiply

90.4

$90.4$ by

9.8

$9.8$ .

sin (x) = \frac{885.92}{4820}

$\sin (x) = \frac{885.92}{4820}$

Step 1.3

Divide

885.92

$885.92$ by

4820

$4820$ .

sin (x) = 0.18380082

$\sin (x) = 0.18380082$

sin (x) = 0.18380082

$\sin (x) = 0.18380082$

Step 2

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

x

$x$ from inside the sine.

x = arcsin (0.18380082)

$x = \arcsin (0.18380082)$

Step 3

Simplify the right side.

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Step 3.1

Evaluate

arcsin (0.18380082)

$\arcsin (0.18380082)$ .

x = 0.18485176

$x = 0.18485176$

x = 0.18485176

$x = 0.18485176$

Step 4

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

π

$π$ to find the solution in the second quadrant.

x = (3.14159265) - 0.18485176

$x = (3.14159265) - 0.18485176$

Step 5

Solve for

x

$x$ .

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Step 5.1

Remove parentheses.

x = 3.14159265 - 0.18485176

$x = 3.14159265 - 0.18485176$

Step 5.2

Remove parentheses.

x = (3.14159265) - 0.18485176

$x = (3.14159265) - 0.18485176$

Step 5.3

Subtract

0.18485176

$0.18485176$ from

3.14159265

$3.14159265$ .

x = 2.95674088

$x = 2.95674088$

x = 2.95674088

$x = 2.95674088$

Step 6

Find the period of

sin (x)

$\sin (x)$ .

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Step 6.1

The period of the function can be calculated using

\frac{2 π}{| b |}

$\frac{2 π}{| b |}$ .

\frac{2 π}{| b |}

$\frac{2 π}{| b |}$

Step 6.2

Replace

b

$b$ with

1

$1$ in the formula for period.

\frac{2 π}{| 1 |}

$\frac{2 π}{| 1 |}$

Step 6.3

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

0

$0$ and

1

$1$ is

1

$1$ .

\frac{2 π}{1}

$\frac{2 π}{1}$

Step 6.4

Divide

2 π

$2 π$ by

1

$1$ .

2 π

$2 π$

2 π

$2 π$

Step 7

The period of the

sin (x)

$\sin (x)$ function is

2 π

$2 π$ so values will repeat every

2 π

$2 π$ radians in both directions.

x = 0.18485176 + 2 π n, 2.95674088 + 2 π n

$x = 0.18485176 + 2 π n, 2.95674088 + 2 π n$ , for any integer

n

$n$