[20!]Sinusoidal functions 1

2013-05-21 7:44 am

1. Find the values of θ from 0∘to 360∘inclusive satisfying the equation
5sin²θ-2sinθ-3cos²θ=0

2. Solve the equation 4sinA=3tanA for 0˚≦A≦360˚.

3. Solve cos(3θ-45˚)=1/2 when 0˚≦x≦360˚.

回答 (1)

50418129

2013-05-21 4:04 pm

✔ 最佳答案

5sin²θ - 2sinθ - 3cos²θ = 0
5sin²θ - 2sinθ - 3(1 - sin²θ) = 0
8sin²θ - 2sinθ - 3 = 0
(4sinθ - 3)(2sinθ + 1) = 0
sinθ = 3/4 or sinθ = -1/2
θ = 48.6˚, 131.4˚, 330˚, 210˚, where 0˚ <= θ <= 360˚

4sinA = 3tanA
4sinAcosA = 3sinA
4sinAcosA - 3sinA = 0
sinA(4cosA - 3) = 0
sinA = 0 or cosA = 3/4
A = 0˚, 180˚, 360˚, 41.4˚, 318.6˚, where 0˚ <= θ <= 360˚

cos(3θ - 45˚) = 1/2
3θ - 45˚ = 60˚, 300˚, 420˚, 660˚, 780˚, 1020˚, where -45˚ <= 3θ - 45˚ <= 1035˚
θ = 35˚, 115˚, 155˚, 235˚, 275˚, 355˚, where 0˚ <= θ <= 360˚

參考: knowledge

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