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Math Help - trig equations

  1. #1
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    trig equations

    1. Which of the following is a solution to the equation 2sin^2x+sinx=1
    I. x=30
    II. x=150
    III. x=270

    a)III only
    b)I and III only
    c) II and III only
    d)I, II, III

    I tried substitution but I dont think it works
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  2. #2
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    Dear ceroseven,

    2sin^{2}x+sinx=1

    When, x=30^{o}\Rightarrow{L.H.S=2sin^{2}30^{o}+Sin30^{o}  =\left(2\times{\frac{1}{4}}\right)+\frac{1}{2}=1}

    When, x=150^{o}\Rightarrow{L.H.S=2sin^{2}150^{o}+Sin150^  {o}=2sin^{2}30^{o}+sin30^{o}}

    Therefore, L.H.S=2sin^{2}150^{o}+Sin150^{o}=\left(2\times{\fr  ac{1}{4}}\right)+\frac{1}{2}=1

    When, x=270^{o}\Rightarrow{L.H.S=2sin^{2}270^{o}+Sin270^  {o}=\left(2\times{-1}\right)+\left(-1\right)=-3}

    Hope this helps.
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  3. #3
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    Quote Originally Posted by ceroseven View Post
    1. Which of the following is a solution to the equation 2sin^2x+sinx=1
    I. x=30
    II. x=150
    III. x=270

    a)III only
    b)I and III only
    c) II and III only
    d)I, II, III

    I tried substitution but I dont think it works
    2\sin^2{x} + \sin{x} = 1

    2\sin^2{x} + \sin{x} - 1 = 0


    Let X = \sin{x} so that the equation becomes

    2X^2 + X - 1 = 0

    2X^2 + 2X - X - 1 = 0

    2X(X + 1) - 1(X + 1) = 0

    (X + 1)(2X - 1) = 0

    X + 1 = 0 or 2X - 1 = 0

    X = -1 or X = \frac{1}{2}.


    So \sin{x} = -1 or \sin{x} = \frac{1}{2}

    x = 270^\circ + 360^\circ n or x = \left\{ 30^\circ, 150^\circ \right\} + 360^\circ n, where n represents the number of times you have gone around the unit circle.


    Can you see which solutions fit now?
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