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Math Help - 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: sec^2\pi x = 4/\pi
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  2. #2
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    Are you sure it's not just

    \sec{(\pi x)} = \frac{4}{\pi}? Because if so, remember that \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 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 ^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: sec^2\pi x = 4/\pi
    Without a calculator i get

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

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

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

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

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

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

     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

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

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

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

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

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

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

     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 x. With the power of 2, like Pickslides said, you can only get an "expression" for 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 x. With the power of 2, like Pickslides said, you can only get an "expression" for 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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