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Math Help - Trigonometry...help needed please!

  1. #1
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    Trigonometry...help needed please!

    When x is between 0 and 2pi
    a) sinx=0.7

    When theta is between negative pi and pi

    a) 6sinthetacostheta-3costheta+2sintheta-1=0

    When theta is between 0 and 2pi

    b)3 cos^2theta-13costheta=sin^2theta-9

    thanks in advance if you can help me
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  2. #2
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    Hello, Confuzzled!

    When 0 ≤ x ≤ 2π

    . . a) . sin x .= .0.7

    You need a calculator for this one.

    . . x .= .Inverse sine of (0.7) . .0.7754, 2.3662 radians.



    When -π ≤ θ ≤ π

    . . a) . 6sinθcosθ - 3cosθ + 2sinθ - 1 .= .0

    Factor: . 3cosθ(2sinθ - 1) + (2sinθ - 1) .= .0

    Factor: . (2sinθ - 1)(3cosθ + 1) .= .0

    We have: . 2sinθ - 1 .= .0 . . sinθ = 1/2 . . θ . .0.524, 2.618

    . . . .and: . 3cosθ + 1 .= .0 . . cosθ = -1/3 . . θ . .1.911, -1.911



    When 0 ≤ θ ≤ 2π

    . . b) . 3cos²θ - 13cosθ .= .sin²θ - 9

    We have: . . . .3cos²θ - 13cosθ .= .1 - cos²θ - 9

    . . .Then: . 4cos²θ - 13cosθ + 8 .= .0


    This does not factor; we need the Quadratic Formula.
    . . . . . . . . . . . . . . __
    . . . . . . . . . .13 ± √41
    . . cosθ . = . ----------- . . 2.4254, 0.8246
    . . . . . . . . . . . . 8

    We have: . cosθ .= .2.4254 . . . no solution!

    . . . .and: . cosθ .= .0.8246 . . θ . .0.6013, 5.6819 radians

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  3. #3
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    Thanks for your help. I’ve attempted to answer the following questions but it seems that I get many answers and I’m not sure if I’m doing it right. Could u help me with the following?:

    For theta being between 0 and 360
    a) sin^2theta=4cos^2theta

    For theta being between pi and 2pi
    b) 4cos^2theta=3
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  4. #4
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    Hello again, Confuzzled!

    a) sin²θ = 4cos²θ . . 0° < θ < 360°

    Divide both sides by cos²θ:

    . . . sin²θ
    . . . ------- .= .4
    . . . cos²θ

    . . . tan²θ .= .4

    . . . .tanθ .= .±2

    . . . . . . θ . .63.4°, 116.6°, 243.4°, 296.6°



    b) 4cos²θ = 3 . . π < θ < 2π

    . . . . . . . . . . . . . . . .3
    We have: . cos²θ .= .---
    . . . . . . . . . . . . . . . .4
    . . . . . . . . . . . . . . . . . _
    . . . . . . . . . . . . . . . . .√3
    Then: . . . . cosθ .= . ± ---
    . . . . . . . . . . . . . . . . . 2

    Therefore: . θ .= .7π/6, 11π/6

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