Evaluate tan((-4pi)/3)

$\tan (\frac{- 4 π}{3})$

Move the negative in front of the fraction.

$\tan (- \frac{(4) π}{3})$

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

$\tan (\frac{2 π}{3})$

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 second quadrant.

$- \tan (\frac{π}{3})$

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

$- \sqrt{3}$

The result can be shown in multiple forms.

Exact Form:

$- \sqrt{3}$

Decimal Form:

$- 1.73205080 \dots$

Evaluate tan((-4pi)/3)

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