Trigonometry Examples

$3 \arctan (2 x) = π$

Divide each term in $3 \arctan (2 x) = π$ by $3$ and simplify.

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Divide each term in $3 \arctan (2 x) = π$ by $3$ .

$\frac{3 \arctan (2 x)}{3} = \frac{π}{3}$

Simplify the left side.

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Cancel the common factor of $3$ .

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Cancel the common factor.

$\frac{3 \arctan (2 x)}{3} = \frac{π}{3}$

Divide $\arctan (2 x)$ by $1$ .

$\arctan (2 x) = \frac{π}{3}$

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

$2 x = \tan (\frac{π}{3})$

Simplify the right side.

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

$2 x = \sqrt{3}$

Divide each term in $2 x = \sqrt{3}$ by $2$ and simplify.

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Divide each term in $2 x = \sqrt{3}$ by $2$ .

$\frac{2 x}{2} = \frac{\sqrt{3}}{2}$

Simplify the left side.

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Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{2 x}{2} = \frac{\sqrt{3}}{2}$

Divide $x$ by $1$ .

$x = \frac{\sqrt{3}}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\sqrt{3}}{2}$

Decimal Form:

$x = 0.86602540 \dots$