Question

Find the x-values that are solutions of the equation 5cot^2x-15=0

Answer 1

First solve for the trig function 'cot'

`cot^2 x = (15)/(5) = 3`

Next take the sqrt of both sides (include plus/minus)

`cot x = \pm √(3)`

Now take reciprocal of both sides, this will change trig function to 'tan'
(cot = 1/tan)


`tan x = \pm (1)/(√(3)) = \pm (√(3))/(3)`

Finally use the unit circle or inverse tan on your calculator to find x.
There will be 4 solutions, one for each quadrant.


`x = (\pi)/(6), (5\pi)/(6), (7\pi)/(6), (11\pi)/(6)`