Precalculus Examples

$\sin (x) = (\frac{4}{13} + \frac{1}{13})$

Step 1

Simplify $\frac{4}{13} + \frac{1}{13}$ .

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Step 1.1

Combine the numerators over the common denominator.

$\sin (x) = \frac{4 + 1}{13}$

Step 1.2

Add $4$ and $1$ .

$\sin (x) = \frac{5}{13}$

Step 2

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

$x = \arcsin (\frac{5}{13})$

Step 3

Simplify the right side.

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Step 3.1

Evaluate $\arcsin (\frac{5}{13})$ .

$x = 0.39479111$

Step 4

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.

$x = (3.14159265) - 0.39479111$

Step 5

Solve for $x$ .

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Step 5.1

Remove parentheses.

$x = 3.14159265 - 0.39479111$

Step 5.2

Remove parentheses.

$x = (3.14159265) - 0.39479111$

Step 5.3

Subtract $0.39479111$ from $3.14159265$ .

$x = 2.74680153$

Step 6

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

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Step 6.1

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

$\frac{2 π}{| b |}$

Step 6.2

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

$\frac{2 π}{| 1 |}$

Step 6.3

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

$\frac{2 π}{1}$

Step 6.4

Divide $2 π$ by $1$ .

$2 π$

Step 7

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

$x = 0.39479111 + 2 π n, 2.74680153 + 2 π n$ , for any integer $n$