Subtract 1, divide by sqrt3, and you get:
tanx = -1/sqrt3
This is true in multiple spots.
With sintheta, you get the same intersection of the x-axis at pm kpi where k is an integer.
costheta is really a pi/2 phase shift of sintheta, so you get the same thing, except it is pi/2 pm kpi instead.
The period of tantheta is every pi since it takes on the domain of both sin and cos combined. The phase shift doesn't cause anything more than the vertical asymptotes in the graph, seeing as how whenever sintheta = pm1, costheta = 0.
You can do this:
-1/sqrt3 = (-1/2)/(sqrt3/2) = -1/cancel(2)*cancel(2)/sqrt3
Therefore, it happens wherever:
sintheta = -1/2 AND costheta = sqrt3/2
That means:
theta = -pi/6 pm (kpi) where k is an integer.
tanx:
graph{tanx [-6.24, 6.244, -3.12, 3.12]}
