Trigonometry Examples

$\tan (- \frac{4 π}{3})$

Step 1

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

$\tan (\frac{2 π}{3})$

Step 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 second quadrant.

$- \tan (\frac{π}{3})$

Step 3

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

$- \sqrt{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \sqrt{3}$

Decimal Form:

$- 1.73205080 \dots$