Trigonometry Examples

$- \frac{π}{6} = \arctan (x)$

Step 1

Rewrite the equation as $\arctan (x) = - \frac{π}{6}$ .

$\arctan (x) = - \frac{π}{6}$

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

Simplify $\tan (- \frac{π}{6})$ .

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Step 3.1.1

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$x = \tan (\frac{11 π}{6})$

Step 3.1.2

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because tangent is negative in the fourth quadrant.

$x = - \tan (\frac{π}{6})$

Step 3.1.3

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:

$x = - 0.57735026 \dots$