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標題:
A.math 三角學(急問)20分
發問:
求下列方程通解,答案以度表示 1. sin 5x=cos 3x 2. tan 5A=cot 4A 3. cos x-3^(1/2)sin x=1 4. 3^(1/2)sin A-cos A=2^(1/2) 5. 4 sin A+5 cos A=3
最佳解答:
1) sin(4x+x) = cos(4x-x) sin4xcosx + cos4xsinx = cos4xcosx + sin4xsinx sin4x (cosx-sinx) = cos4x (cosx-sinx) sin4x = cos4x tan4x = 1 4x = 45 (also, 225, 405.......) 4x = 11.25 (also, 56.25, 101.25......) 3) cosx - √3 sinx = 1 cos^2 x -2√3sinxcosx + 3sin^2 x = 1 (cos^2 x + sin^2 x) -2√3sinxcosx + 2sin^2 x = 1 -2√3sinxcosx + 2sin^2 x = 0 2√3sinxcosx = 2sin^2 x 2√3cosx = 2sinx √3cosx = sinx √3 = tanx x = 60 (also, 240, 420......) 4) √3sinA - cosA = √2 3sin^2 A -2√3sinAcosA + cos^2 A = 2 2sin^2 A -2√3sinAcosA + (cos^2 A + sin^2 A)= 2 2sin^2 A -2√3sinAcosA = 1 -2√3sinAcosA = 1 - 2sin^2 A -2√3sinAcosA = cos2A -√3sin2A = cos2A tan2A = -1/√3 2A = -30 2A = 150 (also, 330, 510.......) A = 75 (also, 165, 255........)
其他解答:
A.math 三角學(急問)20分
發問:
求下列方程通解,答案以度表示 1. sin 5x=cos 3x 2. tan 5A=cot 4A 3. cos x-3^(1/2)sin x=1 4. 3^(1/2)sin A-cos A=2^(1/2) 5. 4 sin A+5 cos A=3
最佳解答:
1) sin(4x+x) = cos(4x-x) sin4xcosx + cos4xsinx = cos4xcosx + sin4xsinx sin4x (cosx-sinx) = cos4x (cosx-sinx) sin4x = cos4x tan4x = 1 4x = 45 (also, 225, 405.......) 4x = 11.25 (also, 56.25, 101.25......) 3) cosx - √3 sinx = 1 cos^2 x -2√3sinxcosx + 3sin^2 x = 1 (cos^2 x + sin^2 x) -2√3sinxcosx + 2sin^2 x = 1 -2√3sinxcosx + 2sin^2 x = 0 2√3sinxcosx = 2sin^2 x 2√3cosx = 2sinx √3cosx = sinx √3 = tanx x = 60 (also, 240, 420......) 4) √3sinA - cosA = √2 3sin^2 A -2√3sinAcosA + cos^2 A = 2 2sin^2 A -2√3sinAcosA + (cos^2 A + sin^2 A)= 2 2sin^2 A -2√3sinAcosA = 1 -2√3sinAcosA = 1 - 2sin^2 A -2√3sinAcosA = cos2A -√3sin2A = cos2A tan2A = -1/√3 2A = -30 2A = 150 (also, 330, 510.......) A = 75 (also, 165, 255........)
其他解答:
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