Precalculus Examples

$3 \tan^{3} (3) = \tan (x)$

Step 1

Rewrite the equation as $\tan (x) = 3 \tan^{3} (3)$ .

$\tan (x) = 3 \tan^{3} (3)$

Step 2

Simplify $3 \tan^{3} (3)$ .

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Step 2.1

Evaluate $\tan (3)$ .

$\tan (x) = 3 \cdot {0.05240777}^{3}$

Step 2.2

Raise $0.05240777$ to the power of $3$ .

$\tan (x) = 3 \cdot 0.00014394$

Step 2.3

Multiply $3$ by $0.00014394$ .

$\tan (x) = 0.00043182$

Step 3

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

$x = \arctan (0.00043182)$

Step 4

Simplify the right side.

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Step 4.1

Evaluate $\arctan (0.00043182)$ .

$x = 0.02474179$

Step 5

The tangent function is positive in the first and third quadrants. To find the second solution, subtract the reference angle from $180$ to find the solution in the fourth quadrant.

$x = 180 + 0.02474179$

Step 6

Add $180$ and $0.02474179$ .

$x = 180.02474179$

Step 7

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

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Step 7.1

The period of the function can be calculated using $\frac{180}{| b |}$ .

$\frac{180}{| b |}$

Step 7.2

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

$\frac{180}{| 1 |}$

Step 7.3

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

$\frac{180}{1}$

Step 7.4

Divide $180$ by $1$ .

$180$

Step 8

The period of the $\tan (x)$ function is $180$ so values will repeat every $180$ degrees in both directions.

$x = 0.02474179 + 180 n, 180.02474179 + 180 n$ , for any integer $n$

Step 9

Consolidate the answers.

$x = 0.02474179 + 180 n$ , for any integer $n$