1. ## Solving Tangent Equation

Hello M.H.F.

I am looking for suggestions on how to solve this Tangent Equation:

tan(x) = -sqrt(3) for [0,2pi]

I can solve this using my graphing calculator by graphing y1 = tan(x) and y2 = -sqrt(3) and using the intersect function to get my answers of 2pi/3 and 5pi/3.

I am really interested to see how I would go about solving this mathematically without graphing. Please advise or show any techniques that you find appropriate.

Thanks,
Jack Daniels

2. Originally Posted by UC151CPR
Hello M.H.F.

I am looking for suggestions on how to solve this Tangent Equation:

tan(x) = -sqrt(3) for [0,2pi]

I can solve this using my graphing calculator by graphing y1 = tan(x) and y2 = -sqrt(3) and using the intersect function to get my answers of 2pi/3 and 5pi/3.

I am really interested to see how I would go about solving this mathematically without graphing. Please advise or show any techniques that you find appropriate.

Thanks,
Jack Daniels
$\tan{x} = -\sqrt{3}$ is a unit circle value.

for $0 \le x < 2\pi$ ...

$\tan\left(\frac{2\pi}{3}\right) = -\sqrt{3}$

and

$\tan\left(\frac{5\pi}{3}\right) = -\sqrt{3}$