標題:
solving trigo equations!Please
發問:
Please help me solve the following trigo equations, please show all the steps and the solutions: 1. sin2θ=0 2. sinθ-cosθ=0 3. 2sin^2θ - cos^2θ = 0 4. sin^2θ+2sinθcosθ+cos2θ=0 If any trigo identities are used, please state it. Thanks!
最佳解答:
Suppose that you are referring to 0 <= θ <= 360: 1) sin 2θ = 0 2θ = 0, 180, 360, 540 or 720 θ = 0, 90, 180, 270 or 360 2) sin θ - cos θ = 0 sin θ = cos θ tan θ = 1 θ = 45 or 225 3) 2 sin2 θ - cos2 θ = 0 2 sin2 θ = cos2 θ tan2 θ = 1/2 tan θ = 1/√2 θ = 35.3 or 215.3 4) sin2 θ + 2 sin θ cos θ + cos 2θ = 0 sin2 θ + 2 sin θ cos θ + cos2 θ - sin2 θ = 0 2 sin θ cos θ + cos2 θ = 0 cos θ (2 sin θ + cos θ) = 0 cos θ = 0 or 2 sin θ + cos θ = 0 cos θ = 0 or tan θ = -1/2 θ = 90 or 270 or 153.4 or 333.4 2010-07-06 18:12:02 補充： For Q3, the identity sin θ/cos θ = tan θ has been used For Q4, the identities sin θ/cos θ = tan θ and cos 2θ = cos^2 θ - sin^2 θ have been used.
其他解答:
1) sin 2θ = 0 2θ = 0 θ = 0 2) sinθ - cosθ = 0 sinθ = cosθ sinθ / cosθ = 1 tanθ = 1 θ = 45 degree 2010-07-06 17:58:20 補充： 3) 2sin^2θ - cos^2θ = 0 2sin^2θ = cos^2θ 2tan^2θ =1 tan^2θ =1 / 2 tanθ = sqrt(0.5) find θ yourself.
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