Homework SourseSin 2x cos 3x 0 0 2 pi cos 2xsinx 12 0 2 piSolutionsin 2
Sin 2x + cos 3x = 0, [0, 2 pi] cos 2x-sinx = 1/2, [0, 2 pi]![Sin 2x + cos 3x = 0, [0, 2 pi] cos 2x-sinx = 1/2, [0, 2 pi]Solutionsin 2 x + cos 3 x = 0 2 sin x cos x + cos 3 x = 0 cos 3x = cos^3 x - 3 sin^2 x cos x cos^3 x](/WebImages/15/sin-2x-cos-3x-0-0-2-pi-cos-2xsinx-12-0-2-pisolutionsin-2-1023486-1761529636-0.webp "Sin 2x + cos 3x = 0, [0, 2 pi] cos 2x-sinx = 1/2, [0, 2 pi]Solutionsin 2 x + cos 3 x = 0 2 sin x cos x + cos 3 x = 0 cos 3x = cos^3 x - 3 sin^2 x cos x cos^3 x")
Solution
sin 2 x + cos 3 x = 0
2 sin x cos x + cos 3 x = 0
cos 3x = cos^3 x - 3 sin^2 x cos x
cos^3 x - 3 sin^2 x cos x + sin x cos x = 0
cosx ( cos^2 x - 3sin^2x + sin x ) = 0
cos x = 0 or ( cos^2 x - 3sin^2x + sin x ) = 0
cos x = 0
x = pi/2 , 3pi/2
( cos^2 x - 3sin^2x + sin x ) = 0
x = 2pi - .31416 , pi + .31416 , pi - .94248 , .94248
