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Thread: Double angles and trig ratios

  1. #1
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    Question Double angles and trig ratios

    Hi,


    I hope someone can help. I'm trying to rewrite the trig ratio cos3x to fit within a double angle formula. These are the steps which I have followed: https://www.algebra.com/algebra/home...on.182274.html

    While I understand the steps listed in the link that I pasted above, it does not provide me with the solution that I'm looking for. The solution for this problem according to my textbook is 2cos^2(1.5x-1).

    Any ideas on how to solve this problem in order for it to match up with the textbook's solution?


    Sincerely,
    Olivia
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  2. #2
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    Re: Double angles and trig ratios

    Why would you have 1.5x - 1?
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    Re: Double angles and trig ratios

    Quote Originally Posted by otownsend View Post
    ... The solution for this problem according to my textbook is 2cos^2(1.5x-1)
    You made an error in typing the expression ... should be $2\cos^2(1.5x)-1$

    Note the double angle identity for cosine ...

    $\cos(2\theta) = 2\cos^2(\theta)-1$

    now, let $\theta = \dfrac{3x}{2}$ ...
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    Re: Double angles and trig ratios

    Okay so you're saying that is one way to solve this is the way which you are describing above, and another way is this https://www.algebra.com/algebra/home...on.182274.html?

    If that is the case then I find it odd that both solutions (solution 1 - 2cos^2(1.5x)-1 and solution 2 - 4cos^3-3cosx look entirely different when I graph them... why is this?
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    Re: Double angles and trig ratios

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    Re: Double angles and trig ratios

    If that is the case then I find it odd that both solutions (solution 1 - 2cos^2(1.5x)-1 and solution 2 - 4cos^3-3cosx look entirely different when I graph them... why is this?
    Maybe you didn't enter each expression correctly into the grapher.

    attached are three graphs, all the same ...

    $\color{blue}{y = \cos(3x)}$

    $y = 2\cos^2(1.5x)-1$

    $\color{red}{y=4\cos^3{x}-3\cos{x}}$
    Attached Thumbnails Attached Thumbnails Double angles and trig ratios-cos-3x-_1.jpg   Double angles and trig ratios-cos-3x-_2.jpg   Double angles and trig ratios-cos-3x-_3.jpg  
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    Re: Double angles and trig ratios

    The reason why I got different graphs was because Desmos doesn't allow any trig ratio with a power larger than 2.

    But now after looking at that link SlipEternal posted, and the graphs skeeter created I definetely see that 4cos^3-3cosx and 2cos^2(1.5x)-1 are the same.

    Thanks for all your help.
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    Re: Double angles and trig ratios

    Quote Originally Posted by otownsend View Post
    The reason why I got different graphs was because Desmos doesn't allow any trig ratio with a power larger than 2.
    It doesn't? ...
    Attached Thumbnails Attached Thumbnails Double angles and trig ratios-img_1597.png  
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