- #1
smallbadwolf
- 14
- 0
okay this problem stumped me for a while but here is my work for it, and I just got stuck at the end so if any help can be provided thanks in advance.
sin3x = sinx
sin(2x + x) = sinx
sin2x cos x + cos2x sinx = sinx
2sinx cosx cosx + (2cos^2(x) -1) sinx = sinx
2sinx cos^2(x) + 2cos^2(x) sinx - sinx = sinx
2sinx cos^2(x) + 2cos^2(x) sinx - 2sinx = 0
2sinx (cos^2(x) + cos^2(x) - 2) = 0
2sinx (2cos^2(x) - 2) = 0
4sinx(cos^2(x) -1) = 0
4sinx(-sin^2(x)) = 0
4sinx = 0 , -sin^2x = 0
x = 0 , x = 0, pi, 2pi
Why is it when I graph the equation sin3x - sinx = 0 on my calculator, it comes with 7 solutions when i only have 3?
sin3x = sinx
sin(2x + x) = sinx
sin2x cos x + cos2x sinx = sinx
2sinx cosx cosx + (2cos^2(x) -1) sinx = sinx
2sinx cos^2(x) + 2cos^2(x) sinx - sinx = sinx
2sinx cos^2(x) + 2cos^2(x) sinx - 2sinx = 0
2sinx (cos^2(x) + cos^2(x) - 2) = 0
2sinx (2cos^2(x) - 2) = 0
4sinx(cos^2(x) -1) = 0
4sinx(-sin^2(x)) = 0
4sinx = 0 , -sin^2x = 0
x = 0 , x = 0, pi, 2pi
Why is it when I graph the equation sin3x - sinx = 0 on my calculator, it comes with 7 solutions when i only have 3?