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Finding the values of trig equations Watch

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    I am using the school's MyMaths login right now, and I'm revising trig equations, but I can't figure out the reason for one of the answers.


    I understand that most of the incorrect answers were rounding errors, but for sin 3θ = -1, I don't understand how to get 1.57 as an answer. I figured out that I can get 3.67 and 5.76 by doing π - (-1/6(π)) and 2π + (-1/6(π)), but I don't understand how to find 1.57.

    How do I find out all the values of θ for sin 3θ = -1?
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    (Original post by ashjack)
    I am using the school's MyMaths login right now, and I'm revising trig equations, but I can't figure out the reason for one of the answers.
    I understand that most of the incorrect answers were rounding errors, but for sin 3θ = -1, I don't understand how to get 1.57 as an answer. I figured out that I can get 3.67 and 5.76 by doing π - (-1/6(π)) and 2π + (-1/6(π)), but I don't understand how to find 1.57.

    How do I find out all the values of θ for sin 3θ = -1?
    \sin(3\theta)=-1 \Rightarrow 3\theta=-\frac{\pi}{2} \Rightarrow \theta=-\frac{\pi}{6}. And of course another solution is given by 3\theta = \pi - (-\frac{\pi}{2})=\frac{3}{2}\pi

    So \theta = \frac{\pi}{2} \approx 1.57

    Then add on 2\pi to both solutions to get 3\theta=2\pi - \frac{\pi}{2} \Rightarrow \theta=\frac{\pi}{2} \approx 1.57 again, and you also have 3\theta=2\pi + \pi - (-\frac{\pi}{2}) \Rightarrow \theta=\frac{7}{6}\pi \approx 3.67

    Then add on 2\pi again to both solutions and the latter should give you your 5.76.
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    (Original post by RDKGames)
    \sin(3\theta)=-1 \Rightarrow 3\theta=-\frac{\pi}{2} \Rightarrow \theta=-\frac{\pi}{6}. And of course another solution is given by 3\theta = \pi - (-\frac{\pi}{2})=\frac{3}{2}\pi

    So \theta = \frac{\pi}{2} \approx 1.57

    Then add on 2\pi to both solutions to get 3\theta=2\pi - \frac{\pi}{2} \Rightarrow \theta=\frac{\pi}{2} \approx 1.57 again, and you also have 3\theta=2\pi + \pi - (-\frac{\pi}{2}) \Rightarrow \theta=\frac{7}{6}\pi \approx 3.67

    Then add on 2\pi again to both solutions and the latter should give you your 5.76.
    Thank you for your reply, I think I understand now. Just to clarify, you used the value of \theta in the original trig equation to find 1.57?
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    (Original post by ashjack)
    Thank you for your reply, I think I understand now. Just to clarify, you used the value of \theta in the original trig equation to find 1.57?
    What do you mean I used \theta ?? I can't really use it when I'm trying to find it.

    I used the fact that solutions to \sin(x)=-1 are given by x=2\pi n -\frac{\pi}{2} and x=2\pi n + \pi - (-\frac{\pi}{2}) from small integers n (in this case n=0,1,2)

    If you let x=3\theta then you have 3\theta = 2\pi n - \frac{\pi}{2} and 3\theta=2\pi n +\frac{3\pi}{2}

    Then you can solve for \theta in your wanted range.
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    (Original post by RDKGames)
    What do you mean I used \theta ?? I can't really use it when I'm trying to find it.

    I used the fact that solutions to \sin(x)=-1 are given by x=2\pi n -\frac{\pi}{2} and x=2\pi n + \pi - (-\frac{\pi}{2}) from small integers n (in this case n=0,1,2)

    If you let x=3\theta then you have 3\theta = 2\pi n - \frac{\pi}{2} and 3\theta=2\pi n +\frac{3\pi}{2}

    Then you can solve for \theta in your wanted range.
    Thank you, I do understand now. I just need to work on knowing which number to add to and which to take away from when using a Sine graph
 
 
 
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