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Math Help - Inverse trig from an exam paper

  1. #1
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    Inverse trig from an exam paper

    See the image for details. I solved the first two parts and got stuck on the last part.
    Attached Thumbnails Attached Thumbnails Inverse trig from an exam paper-capture1.png  
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    Re: Inverse trig from an exam paper

    Quote Originally Posted by bbrain View Post
    See the image for details. I solved the first two parts and got stuck on the last part.
    Please note that long-standing MHF policy prohibits assistance on exam questions.
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    Re: Inverse trig from an exam paper

    Quote Originally Posted by skeeter View Post
    Please note that long-standing MHF policy prohibits assistance on exam questions.
    Unless it's a past exam or a practice exam. Is it?
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    Re: Inverse trig from an exam paper

    Quote Originally Posted by Prove It View Post
    Unless it's a past exam or a practice exam. Is it?
    Yes, it is. CIE Pre U june 2010
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    Re: Inverse trig from an exam paper

    Well for the first, you'll need to make use of the following identities:

    \displaystyle \begin{align*} \tan{x} &\equiv \frac{\sin{x}}{\cos{x}} \\ \\ \sin{2x} &\equiv 2\sin{x}\cos{x} \\ \\ \cos{2x} &\equiv \cos^2{x} - \sin^2{x} \\ \\ \sin^2{x} + \cos^2{x} &\equiv 1 \\ \\ \tan{\left(\alpha + \beta\right)} &\equiv \frac{\tan{\alpha} + \tan{\beta}}{1 - \tan{\alpha}\tan{\beta}}\end{align*}

    Start by writing \displaystyle \begin{align*} \tan{3\theta} = \tan{\left(2\theta + \theta\right)}\end{align*}. What do you think you would do from here?
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    Re: Inverse trig from an exam paper

    Quote Originally Posted by Prove It View Post
    Well for the first, you'll need to make use of the following identities:

    \displaystyle \begin{align*} \tan{x} &\equiv \frac{\sin{x}}{\cos{x}} \\ \\ \sin{2x} &\equiv 2\sin{x}\cos{x} \\ \\ \cos{2x} &\equiv \cos^2{x} - \sin^2{x} \\ \\ \sin^2{x} + \cos^2{x} &\equiv 1 \\ \\ \tan{\left(\alpha + \beta\right)} &\equiv \frac{\tan{\alpha} + \tan{\beta}}{1 - \tan{\alpha}\tan{\beta}}\end{align*}

    Start by writing \displaystyle \begin{align*} \tan{3\theta} = \tan{\left(2\theta + \theta\right)}\end{align*}. What do you think you would do from here?
    I have already done the first part. It's the last part I am stuck on.
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    Re: Inverse trig from an exam paper

    Quote Originally Posted by bbrain View Post
    I have already done the first part. It's the last part I am stuck on.
    Why didn't I know that? I guess my psychic powers must be a little off today...
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    Re: Inverse trig from an exam paper

    Quote Originally Posted by Prove It View Post
    Why didn't I know that? I guess my psychic powers must be a little off today...
    Anyway could you please help me with the last part?
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