Solve -tan^2(pi/6)

$$- \tan ^ { 2 } ( \frac { \pi } { 6 } )$$

Evaluate

$$-\frac{1}{3}\approx -0.333333333$$

Solution Steps

Get the value of \tan(\frac{\pi }{6}) from trigonometric values table.

$$-\left(\frac{\sqrt{3}}{3}\right)^{2}$$

To raise \frac{\sqrt{3}}{3} to a power, raise both numerator and denominator to the power and then divide.

$$-\frac{\left(\sqrt{3}\right)^{2}}{3^{2}}$$

The square of \sqrt{3} is 3.

$$-\frac{3}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$-\frac{3}{9}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

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

Factor

$$-\frac{1}{3} = -0.3333333333333333$$