Solve tan(7pi/6)=

$$\tan ( \frac { 7 \pi } { 6 } ) =$$

Evaluate

$$\frac{\sqrt{3}}{3}\approx 0.577350269$$

Solution Steps

Use \tan(x+y)=\frac{\tan(x)+\tan(y)}{1-\tan(x)\tan(y)} where x=\pi and y=\frac{\pi }{6} to obtain the result.

$$\tan(\pi +\frac{\pi }{6})=\frac{\tan(\pi )+\tan(\frac{\pi }{6})}{1-\tan(\pi )\tan(\frac{\pi }{6})}$$

Get the value of \tan(\pi ) from trigonometric values table. Replace the value in both the numerator and the denominator.

$$\frac{0+\tan(\frac{\pi }{6})}{1-0\tan(\frac{\pi }{6})}$$

Get the value of \tan(\frac{\pi }{6}) from trigonometric values table. Replace the value in both the numerator and the denominator.

$$\frac{0+\frac{\sqrt{3}}{3}}{1-0\times \frac{\sqrt{3}}{3}}$$

Do the calculations.

$$\frac{\sqrt{3}}{3}$$