Solving trig equations

Question

tan(thetha) +√3=0 

 

When I move the radical 3 to the rIght side, it becomes negative. I dont know how to solve when its negative. 

 

The question is asking to find exact solutions between [ 0, 360) degrees

Answer 1

tan(θ) = -√(3)

 

Since the value of the tangent is negative, then θ is either in the Quadrant 2 or Quadrant 4

 

Then θ = 120° or 300°

Answer 2

You are right, the tan(theta) is a negative number. In fact,  theta = atan(-√3) = -1.047 radians

 

For converting from radians to DEG you use:   180* (-1.047)/pi  = -60 deg

 

Because it is a negative angle, we are located in the four quadrant. But we can convert it to a positive angle just adding 360 deg as follows:

 

Equivalent angle (between 0-360 deg) = 360 - 60  = 300 deg

 

I hope it help you.