More Trigonometric Equations...?

Question

I need help with these... please explain how to find the answers to these...and if the answers if you would like...

I have to solve the equations and provide a solution set...
EX: cosx = 1/2
Solution set [pi/3 , 5pi/3]
I also need them all in radian bc me interval is 0 less than or equal to x less than 360

1.) tan x + sq.root 3 = 0

2.) 2sin^2x - 3sin x + 1 = 0

3.) 2cos^2x + cos x - 1 = 0

For number 4 I have to find the general solution for the problem... (there is no interval)

4.) 0 = cos^2x - 5cosx + 1

thank you

Answer 1

1.) tan x + sq.root 3 = 0
tan x = -√3
x = [2π/3, 5π/3]

2.) The trick here is to realize that you can substitute for x so that you can do the quadratic formula.
2sin^2x - 3sin x + 1 = 0
let u = sin x
2u^2 - 3u + 1 = 0
Quadratic formula:
u = (-b +/- (b^2 - 4ac)^1/2)/2a
u = (3 +/- (9 - 8)^1/2)/4
u = 3/4 +/- 1/4
u = 1/2, 1
sin x = 1/2 when x = π/6, 5π/6
sin x = 1 when x = π/2
x = [π/6, π/2, 5π/6]

3.) Solve the same way as #2.

4.) Again, same method as #2.