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Thread: Solve for x

  1. #1
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    Solve for x

    Hello,
    I have summer homework and I'm very rusty on how to do some of the trigonometry problems as I haven't done anything like this in months. So if someone could even just point me in the right direction with this problem I would be very grateful. Thanks!

    Solve for x, without a calculator: $\displaystyle sec^2\pi x = 4/\pi$
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  2. #2
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    Are you sure it's not just

    $\displaystyle \sec{(\pi x)} = \frac{4}{\pi}$? Because if so, remember that $\displaystyle \sec{X} = \frac{1}{\cos{X}}$, then you should be able to get an equation you recognise...
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  3. #3
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    It's definitely $\displaystyle sec^2\pi x$. A lot of the problems on this assignment have seemed like they are "trick" problems already, designed to tempt kids into taking some kind of mathematically incorrect shortcut to solve, so I wouldn't put it past the teacher to throw the $\displaystyle ^2$ in there just to see if someone takes the bait.
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  4. #4
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    Quote Originally Posted by Club View Post

    Solve for x, without a calculator: $\displaystyle sec^2\pi x = 4/\pi$
    Without a calculator i get

    $\displaystyle \sec^2\pi x = \frac{4}{\pi}$

    $\displaystyle \sec\pi x = \sqrt{\frac{4}{\pi}}$

    $\displaystyle \sec\pi x = \frac{2}{\sqrt{\pi}}$

    $\displaystyle \frac{1}{\cos\pi x} = \frac{2}{\sqrt{\pi}}$

    $\displaystyle \cos\pi x = \frac{\sqrt{\pi}}{2}$

    $\displaystyle \pi x = \cos^{-1}\frac{\sqrt{\pi}}{2}$

    $\displaystyle x =\frac{ \cos^{-1}\frac{\sqrt{\pi}}{2}}{\pi}$
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  5. #5
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    Quote Originally Posted by pickslides View Post
    Without a calculator i get

    $\displaystyle \sec^2\pi x = \frac{4}{\pi}$

    $\displaystyle \sec\pi x = \sqrt{\frac{4}{\pi}}$

    $\displaystyle \sec\pi x = \frac{2}{\sqrt{\pi}}$

    $\displaystyle \frac{1}{\cos\pi x} = \frac{2}{\sqrt{\pi}}$

    $\displaystyle \cos\pi x = \frac{\sqrt{\pi}}{2}$

    $\displaystyle \pi x = \cos^{-1}\frac{\sqrt{\pi}}{2}$

    $\displaystyle x =\frac{ \cos^{-1}\frac{\sqrt{\pi}}{2}}{\pi}$
    If it didn't have the power of 2, you would be able to find the exact value for $\displaystyle x$. With the power of 2, like Pickslides said, you can only get an "expression" for $\displaystyle x$.
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  6. #6
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    Quote Originally Posted by Prove It View Post
    If it didn't have the power of 2, you would be able to find the exact value for $\displaystyle x$. With the power of 2, like Pickslides said, you can only get an "expression" for $\displaystyle x$.
    What do you mean exactly?
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  7. #7
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    Never mind, I made a mistake...
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