Solving trig

[keroro]

Recently my teacher started the trig unit and without much help he told us to do 6 questions and to be handed in the next day
With limited knowledge of the trigonometry unit i was wondering you any of you guys can help me with these questions

Solve
1) cosx (2sinx + squareroot3)(-squareroot2 cosx - 1) = 0 for 0< = x < = 2pie
2) sin^2x + 2cosx - 2 = 0 for 0< = x < = 2pie
3) 2sinxtanx + tanx - 2sinx - 1 = 0 for 0< = x < = 2pie
4) 6tan^2x - 4sin^2x = 1 for 0< = x < = 2pie


Much Help appreciated, thanks

 

[DrMike]

Remember :

"if ab=0, then either a=0 or b=0"

This helps you solve the first one (and the others too, after a bit of work)

for the second, you might like to remember that sin[sup:291gmxdk]2[/sup:291gmxdk]x+cos[sup:291gmxdk]2[/sup:291gmxdk]x=1 (hint - rearrage this so that only the sin[sup:291gmxdk]2[/sup:291gmxdk]x is on the left hand side)

for the third and fourth, remember that tan x = sin x / cos x

You'll also need to know some common values of sine and cosine :

cos(0) = sin(pi/2) = 1 = sqrt(4)/2
cos(pi/6) = sin(pi/3) = sqrt(3)/2 = sqrt(3)/2
cos(pi/4) = sin(pi/4) = 1/sqrt(2) = sqrt(2)/2
cos(pi/3) = sin(pi/6) = 1/2 = sqrt(1)/2
cos(pi/2) = sin(0) = 0 = sqrt(0)/2

and so on for other values in the range [0,2pi]