Trigonometry Examples

$18 \arctan (x) = 3 π$

Step 1

Divide each term in $18 \arctan (x) = 3 π$ by $18$ and simplify.

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Step 1.1

Divide each term in $18 \arctan (x) = 3 π$ by $18$ .

$\frac{18 \arctan (x)}{18} = \frac{3 π}{18}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $18$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{18 \arctan (x)}{18} = \frac{3 π}{18}$

Step 1.2.1.2

Divide $\arctan (x)$ by $1$ .

$\arctan (x) = \frac{3 π}{18}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Cancel the common factor of $3$ and $18$ .

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Step 1.3.1.1

Factor $3$ out of $3 π$ .

$\arctan (x) = \frac{3 (π)}{18}$

Step 1.3.1.2

Cancel the common factors.

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Step 1.3.1.2.1

Factor $3$ out of $18$ .

$\arctan (x) = \frac{3 π}{3 \cdot 6}$

Step 1.3.1.2.2

Cancel the common factor.

$\arctan (x) = \frac{3 π}{3 \cdot 6}$

Step 1.3.1.2.3

Rewrite the expression.

$\arctan (x) = \frac{π}{6}$

Step 2

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

$x = \tan (\frac{π}{6})$

Step 3

Simplify the right side.

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Step 3.1

The exact value of $\tan (\frac{π}{6})$ is $\frac{\sqrt{3}}{3}$ .

$x = \frac{\sqrt{3}}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\sqrt{3}}{3}$

Decimal Form:

$x = 0.57735026 \dots$