Question

3sinx-2cosx=o; find G s

Answer 1

huh? HUH?
Do you want to find solutions to the equation
3sinx - 2cosx = 0 ?
since 3^2+2^2 = 13, this is equivalent to
√13 (3/√13 sinx - 2/√13 cosx) = 0
Now, let y be the angle such that cosy = 3/√13. Then siny = 2/√13. Now you have
√13 (sinx cosy - cosx siny) = 0
√13 sin(x-y) = 0
So, x-y=0 or x-y = π
That is, x-y = kπ for any integer k.
Thus, x = kπ + arcsin(2/√13)

Answer 2

OR

3 sin x - 2 cos x = 0

3 sin x = 2 cos x

3 sin x / cos x = 2

3 tan x = 2

tan x = 2 / 3

x = k π + tan⁻¹ ( 2 / 3 )

x = k π + arctan ( 2 / 3 )


k π + arctan ( 2 / 3 ) and x = k π + arcsin ( 2 / √13 )

is the same solution is written in a different way.

Answer 3

much simpler, Bosnian. I missed that one, fer shure!