Solve tan(-210^circ)

$$\tan ( - 210 ^ { \circ } )$$

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=180 and y=30 to obtain the result.

$$\tan(180+30)=\frac{\tan(180)+\tan(30)}{1-\tan(180)\tan(30)}$$

Get the value of \tan(180) from trigonometric values table. Replace the value in both the numerator and the denominator.

$$\frac{0+\tan(30)}{1-0\tan(30)}$$

Get the value of \tan(30) 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.

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