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標題:

F.4 A.Maths Trigo Question

發問:

Solve the following equations for 0≦x≦360 1.sinx-sin3x=cosx-cos3x 2.sinx+sin3x+sin5x=0 THX

最佳解答:

1 sinx - sin3x = cosx - cos3x sin3x - sinx = cos3x - cosx 2cos[(3x + x)/2]sin[(3x - x)/2] = -2sin[(3x + x)/2]sin[(3x - x)/2] cos2xsinx = -sin2xsinx sinx(cos2x + sin2x) = 0 sinx = 0 or cos2x + sin2x = 0 sinx = 0 or tan2x = -1 x = 0?, 180? or 360?, or 2x = 135?, 315?, 495? or 675? x = 0?, 67.5?, 157.5?, 180?, 247.5?, 337.5? or 360? 2 sinx+sin3x+sin5x=0 (sinx+sin5x)+sin3x=0 2sin[(5x+x)/2]cos[(5x-x)/2]+sin3x=0 2sin3xcos2x+sin3x=0 sin3x(2cos2x+1)=0 sin3x=0 or cos2x=-1/2 3x=0,180,360,540,720,900,1080 or 2x=120,240,480,600 x=0,60,120,180,240,300,360 or x=60,120,240,300 x=0,60,120,180,240,300,360

其他解答:A9A39959EDCC7BE3