Question
Find all solutions in the interval [0,2π)
sin3x−sinx=0
sin3x−sinx=0
Answers
Damon
Identity:
sin 3θ = 3 sin θ -4 sin^3 θ
so
3 sin x - 4 sin^3 x = sin x
Immediately this is true when x = 0
where else?
3 - 4 sin^2 x = 1
2 = 4 sin^2 x
sin^2 x = 1/2
sin x = + or - 1/sqrt2
LOL try 45 degrees, 135 degrees, 225 and 315 (convert those to radians )
sin 3θ = 3 sin θ -4 sin^3 θ
so
3 sin x - 4 sin^3 x = sin x
Immediately this is true when x = 0
where else?
3 - 4 sin^2 x = 1
2 = 4 sin^2 x
sin^2 x = 1/2
sin x = + or - 1/sqrt2
LOL try 45 degrees, 135 degrees, 225 and 315 (convert those to radians )