The solution set of the mathematical equation sin 3x = sin 2x in senior one What is the solution set of the equation sin3x = sin2x

The solution set of the mathematical equation sin 3x = sin 2x in senior one What is the solution set of the equation sin3x = sin2x

(1) According to the image, when sin3x = sin2x, 3x = pie - 2x, so 5x = pie, x = K1 / 5 pie (k belongs to n)
(2) When sin3x = sin2x, 3x = 2x + 2K, so x = 2K
To sum up, x = k * 1 / 5 faction or x = 2K faction

The solution set of the equation sin2x = SiNx in (- π, π) is

sin2x＝sinx
So 2sinxcosx SiNx = 0
So SiNx (2cosx-1) = 0
Because the domain is (- π, π)
So SiNx = 0 or cosx = 1 / 2
So x = 0, - π / 3, π / 3

What is the number of solutions of the equation sin2x = SiNx in the interval (0,2 π)?
Please use the image solution of y = sin2x, y = SiNx

Y = SiNx in the interval (0,2 π) and X-axis three intersections 0, π, 2 π
Y = sin2x in the interval (0,2 π) and six intersections of X axis 0, π / 2, π, 3 π / 2,2 π
First, there are three solutions, 0, π, 2 π
In addition, the curve has two solutions at (0, π / 2) (0, π / π 2), totally five solutions