Precalculus Examples

$\tan (\frac{7 π}{4}) - \tan (\frac{7 π}{6})$

Step 1

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.

$- \tan (\frac{π}{4}) - \tan (\frac{7 π}{6})$

Step 2

The exact value of $\tan (\frac{π}{4})$ is $1$ .

$- 1 \cdot 1 - \tan (\frac{7 π}{6})$

Step 3

Multiply $- 1$ by $1$ .

$- 1 - \tan (\frac{7 π}{6})$

Step 4

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$- 1 - \tan (\frac{π}{6})$

Step 5

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

$- 1 - \frac{\sqrt{3}}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- 1 - \frac{\sqrt{3}}{3}$

Decimal Form:

$- 1.57735026 \dots$