Question

Directions: Find the Location on Unit Circle, Period & General Solution for this problem>>>>>>> sin^2x=3cos^2x


What I have so far:

sin^2x=3cos^2
sin^2x/cos^2=3
tan^2x=3
tanx=+and- sqrt3

Answer 1

If you haven't already done so, you must memorize the basic trig rations of the 30-6-90° right-angled triangle, as well as the 45-45-90 triangle
I often make a quick sketch of those and it is then easy to get those trig ratios
you should recognize that tan60° = √3
and since tanx = ±√3 , you also know from the CAST rule that x must be in all 4 quadrants
so x = 60, 120, 240, and 300°
or
π/3, 2π/3, 4π/3 and 5π/3

the location of those angles are
(1,√3) , (-1,√3) ..... (you find the other two)

the period of tanx is π
so general solutions:
π/3 + kπ
2π/3 + kπ , where k is an integer