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Math Help - Help with Calc problem....

  1. #1
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    Help with Calc problem....

    alright...so here I am trying to figure out a step in my Calculus problem, and I somehow need to go from sec(squared)[pi/4] = (Square root 2)(squared) = 2.....could anyone explain this?
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    Hello,

    Quote Originally Posted by CALsunshine View Post
    alright...so here I am trying to figure out a step in my Calculus problem, and I somehow need to go from sec(squared)[pi/4] = (Square root 2)(squared) = 2.....could anyone explain this?
    \begin{aligned} \sec^2 \frac{\pi}{4} &=\frac{1}{\cos^2 \frac{\pi}{4}} \\<br />
&=\frac{1}{\left(\frac{\sqrt{2}}{2}\right)^2} \end{aligned}

    \begin{aligned} \sec^2 \frac{\pi}{4} &=\left(\frac{2}{\sqrt{2}}\right)^2 \\<br />
&=\left(\frac{\sqrt{2}\cdot {\color{red}\sqrt{2}}}{\color{red} \sqrt{2}}\right)^2 \\<br />
&=(\sqrt{2})^2 \end{aligned}
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    Quote Originally Posted by CALsunshine View Post
    alright...so here I am trying to figure out a step in my Calculus problem, and I somehow need to go from sec(squared)[pi/4] = (Square root 2)(squared) = 2.....could anyone explain this?
    sec^2 \left ( \frac{\pi}{4} \right )

    = \frac{1}{cos^2 \left ( \frac{\pi}{4} \right ) }

    = \frac{1}{\left ( \frac{\sqrt{2}}{2} \right ) ^2}

    = \frac{1}{\frac{1}{2}}

    = 2

    -Dan
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    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by CALsunshine View Post
    alright...so here I am trying to figure out a step in my Calculus problem, and I somehow need to go from sec(squared)[pi/4] = (Square root 2)(squared) = 2.....could anyone explain this?
    \sec^{2}\left(\frac{\pi}{4}\right)

    Recall that \sec u=\frac{1}{\cos u} and \cos \left(\frac{\pi}{4}\right)=\frac{1}{\sqrt{2}}. Thus, we see then that sec\left(\frac{\pi}{4}\right)=\frac{1}{\frac{1}{\s  qrt{2}}}=\sqrt{2}.

    Therefore, \sec^{2}\left(\frac{\pi}{4}\right)=\left(\sqrt{2}\  right)^2=2.

    Hope that answers your question!!
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    Thanks guys!!!! I totally forgot to use my unit circle....that would have made my life a lot easier!
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