trigonometry equations

[fiery123]

Solve the equation sin^2(x) - sinxcosx = 6cos^2(x)for 0<=x<=360

I factorised it but cannot find the answer.

(sinx+2cosx)(sinx-3cosx)=0

[Glaysher]

sin x + 2 cos x = 0 or sin x - 3 cos x = 0

sin x = -2 cos x or sin x = 3 cos x

tan x = -2 or tan x = 3

Solve for x

[fiery123]

thank you thank you , i should have known such an easy question.

[fiery123]

answer to previous question. 296.6, 71.6, 117, 251.56

I also want to ask another question, also an trigonometry equation. These are not homework questions or anything, its just that im studying this topic by myself.

solve 5 tanx - 3 cosx = 0

My working.
(5sinx)/cosx - 3cosx = 0
(5sinx-3cos^2(x))/cosx = 0
5sinx - 3cos^2x = 0
5sinx = 3cos^2x
sinx/cos^2x = 3/5
tanx/cosx = 3/5
tanx = 3 cosx = 5
x=71.6 or 251.56

Which is wrong, so i need some help.

[Glaysher]

5 sin x = 3 cos² x
5 sin x = 3(1 - sin² x)
5 sin x = 3 - 3 sin² x
3 sin² x + 5 sin x - 3 = 0

sin x = [-5 +/- \sqrt{25 + 36}]/6

[fiery123]

right thanks.