Precalculus Examples

$\frac{1}{5} \cdot \sin (x) = 0.04$

Step 1

Multiply both sides of the equation by $5$ .

$5 (\frac{1}{5} \sin (x)) = 5 \cdot 0.04$

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

Simplify $5 (\frac{1}{5} \sin (x))$ .

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Step 2.1.1.1

Combine $\frac{1}{5}$ and $\sin (x)$ .

$5 \frac{\sin (x)}{5} = 5 \cdot 0.04$

Step 2.1.1.2

Cancel the common factor of $5$ .

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Step 2.1.1.2.1

Cancel the common factor.

$5 \frac{\sin (x)}{5} = 5 \cdot 0.04$

Step 2.1.1.2.2

Rewrite the expression.

$\sin (x) = 5 \cdot 0.04$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $5$ by $0.04$ .

$\sin (x) = 0.2$

Step 3

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

$x = \arcsin (0.2)$

Step 4

Simplify the right side.

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Step 4.1

Evaluate $\arcsin (0.2)$ .

$x = 0.20135792$

Step 5

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

$x = (3.14159265) - 0.20135792$

Step 6

Solve for $x$ .

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Step 6.1

Remove parentheses.

$x = 3.14159265 - 0.20135792$

Step 6.2

Remove parentheses.

$x = (3.14159265) - 0.20135792$

Step 6.3

Subtract $0.20135792$ from $3.14159265$ .

$x = 2.94023473$

Step 7

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

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Step 7.1

The period of the function can be calculated using $\frac{2 π}{| b |}$ .

$\frac{2 π}{| b |}$

Step 7.2

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

$\frac{2 π}{| 1 |}$

Step 7.3

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

$\frac{2 π}{1}$

Step 7.4

Divide $2 π$ by $1$ .

$2 π$

Step 8

The period of the $\sin (x)$ function is $2 π$ so values will repeat every $2 π$ radians in both directions.

$x = 0.20135792 + 2 π n, 2.94023473 + 2 π n$ , for any integer $n$