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Math Help - Where the hell is my mistake

  1. #1
    Member dokrbb's Avatar
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    Where the hell is my mistake

    I have to find f'(x) and f'(1) for f(x) = cos(x) - 2tan(x)

    f'(x) = -sin(x) - 2sec^2(x)

    finding values of x I evaluate sin^(-1)(x), in this case sin^(-1)(1), am I right?

    f'(1) = -sin(x) - 2sec^2(x) = -sin(x) - 2(1+ cot^2(1)) = -sin(1) - 2(1+ 1/tan^2(1)) = -1.570796327 - 2(1+1/0.616850275) = .....

    I don't get where is my mistake, can someone show me?

    Thanks
    Last edited by dokrbb; April 8th 2013 at 04:34 PM.
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  2. #2
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    Re: Where the hell is my mistake

    If \displaystyle f'(x) = -\sin{(x)} - 2\sec^2{(x)}, then \displaystyle f'(1) = -\sin{(1)} - 2\sec^2{(1)}, remembering that your angles will be measured in radians. I have no idea why you are suggesting using inverse trigonometric functions.

    If you need help evaluating the sec values, rewrite \displaystyle \sec{(x)} = \frac{1}{\cos{(x)}}.
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    Re: Where the hell is my mistake

    Quote Originally Posted by Prove It View Post
    If \displaystyle f'(x) = -\sin{(x)} - 2\sec^2{(x)}, then \displaystyle f'(1) = -\sin{(1)} - 2\sec^2{(1)}, remembering that your angles will be measured in radians. I have no idea why you are suggesting using inverse trigonometric functions.

    If you need help evaluating the sec values, rewrite \displaystyle \sec{(x)} = \frac{1}{\cos{(x)}}.
    In this case would it be right in this way,

    \displaystyle f'(1) = -\sin{(1)} - 2\sec^2{(1)} = -\sin{(1)} - 2\frac{1}{\cos{(1)}} = -\sin{(1)} - 0

    which finally gives me -0.841470984radians = -48.21273601degrees

    or I'm missing something from basic trigonometry? I'm really frustrated...
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  4. #4
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    Re: Where the hell is my mistake

    You are trying to get a numerical value, not an angle. Just plug this into your calculator AS IS. Do NOT use inverse trigonometric functions. I have no idea why you got that 2/cos(1) is 0...
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  5. #5
    Member dokrbb's Avatar
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    Re: Where the hell is my mistake

    Quote Originally Posted by Prove It View Post
    You are trying to get a numerical value, not an angle. Just plug this into your calculator AS IS. Do NOT use inverse trigonometric functions. I have no idea why you got that 2/cos(1) is 0...
    that simple -7.692508626 , oh my god
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