Precalculus Examples

$\tan (x) = 5$

Step 1

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

$x = \arctan (5)$

Step 2

Simplify the right side.

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Step 2.1

Evaluate $\arctan (5)$ .

$x = 1.37340076$

Step 3

The tangent function is positive in the first and third quadrants. To find the second solution, add the reference angle from $π$ to find the solution in the fourth quadrant.

$x = (3.14159265) + 1.37340076$

Step 4

Solve for $x$ .

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Step 4.1

Remove parentheses.

$x = 3.14159265 + 1.37340076$

Step 4.2

Remove parentheses.

$x = (3.14159265) + 1.37340076$

Step 4.3

Add $3.14159265$ and $1.37340076$ .

$x = 4.51499342$

Step 5

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

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Step 5.1

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

$\frac{π}{| b |}$

Step 5.2

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

$\frac{π}{| 1 |}$

Step 5.3

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

$\frac{π}{1}$

Step 5.4

Divide $π$ by $1$ .

$π$

Step 6

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

$x = 1.37340076 + π n, 4.51499342 + π n$ , for any integer $n$

Step 7

Consolidate $1.37340076 + π n$ and $4.51499342 + π n$ to $1.37340076 + π n$ .

$x = 1.37340076 + π n$ , for any integer $n$