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Math Help - Pre-Calc Homework Question

  1. #1
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    Question Pre-Calc Homework Question

    A problem from my homework:

    Explain why sin(18degrees)=cos(72degrees). Then using the previous problem, explain why:

    (8t^4)-(8t^2)-t+1=0

    Thank You!
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  2. #2
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    Re: Pre-Calc Homework Question

    Quote Originally Posted by jonathanraxa View Post
    A problem from my homework:

    Explain why sin(18degrees)=cos(72degrees). Then using the previous problem, explain why:

    (8t^4)-(8t^2)-t+1=0

    Thank You!
    Draw any right-angle triangle. Call one of the non-right angles \displaystyle \begin{align*} \theta^{\circ} \end{align*}, then the other angle is \displaystyle \begin{align*} 90^{\circ} - \theta^{\circ} \end{align*}. Do you understand why? The three angles in a triangle have to add to \displaystyle \begin{align*} 180^{\circ} \end{align*}.

    Now note that from the point of view of each angle, the hypotenuses are the same, but the opposite and adjacent sides switch.

    So \displaystyle \begin{align*} \sin{\left(90^{\circ} - \theta^{\circ}\right)} = \cos{\theta^{\circ}} \end{align*} and \displaystyle \begin{align*} \cos{\left(90^{\circ} - \theta^{\circ}\right)} = \sin{\theta^{\circ}} \end{align*}.
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  3. #3
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    Re: Pre-Calc Homework Question

    Ok I got that thanks. As for the second portion, given that:
    t=sin(18degrees)
    what are the steps in solving:
    (8t^4)-(8t^2)-t+1=0 ?
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    Re: Pre-Calc Homework Question

    Quote Originally Posted by jonathanraxa View Post
    A problem from my homework:

    Explain why sin(18degrees)=cos(72degrees). Then using the previous problem, explain why:

    (8t^4)-(8t^2)-t+1=0

    Thank You!
    What is t being used to represent?
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  5. #5
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    Re: Pre-Calc Homework Question

    I'm plugging sin(18degrees) in for t in the equation.
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    Re: Pre-Calc Homework Question

    Pre-Calc Homework Question-msp29161a18ha859a3d752b000050379ie68eda0de3.gif

    I want to find out how this is true. I don't know where to begin =/
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