Solve tan(4pi/3)

$$\tan ( \frac { 4 \pi } { 3 } )$$

Evaluate

$$\sqrt{3}\approx 1.732050808$$

Solution Steps

Use \tan(x+y)=\frac{\tan(x)+\tan(y)}{1-\tan(x)\tan(y)} where x=\pi and y=\frac{\pi }{3} to obtain the result.

$$\tan(\pi +\frac{\pi }{3})=\frac{\tan(\pi )+\tan(\frac{\pi }{3})}{1-\tan(\pi )\tan(\frac{\pi }{3})}$$

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

$$\frac{0+\tan(\frac{\pi }{3})}{1-0\tan(\frac{\pi }{3})}$$

Get the value of \tan(\frac{\pi }{3}) from trigonometric values table. Replace the value in both the numerator and the denominator.

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

Do the calculations.

$$\sqrt{3}$$