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Math Help - Determining equations for secant/cosecant curves.

  1. #1
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    Determining equations for secant/cosecant curves.

    I have a question on my homework that I don't really understand, and the textbook isn't helping me at all, I was hoping any of you could. I was ill and still haven't gotten the notes I've missed, but the test is 2 days away

    Can someone tell me the steps I need to do in order to figure this out? I'm really having trouble with it.




    Thanks to everyone in advance!
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  2. #2
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    Hello Random-Hero-
    Quote Originally Posted by Random-Hero- View Post
    I have a question on my homework that I don't really understand, and the textbook isn't helping me at all, I was hoping any of you could. I was ill and still haven't gotten the notes I've missed, but the test is 2 days away

    Can someone tell me the steps I need to do in order to figure this out? I'm really having trouble with it.




    Thanks to everyone in advance!
    This is what you need to know:

    (1) \sec(x) = \frac{1}{\cos(x)}

    (2) \cos (x) =0 when x = \frac{\pi}{2}, \frac{3\pi}{2},\frac{5\pi}{2},...

    So for these values of x, \sec(x) does not exist.

    (3) The maximum value of \cos(x) is 1, and this occurs when x = 0, 2\pi, 4\pi, ...

    So the minimum positive value of \sec(x) is 1 at these values of x.

    Similarly, the maximum negative value of \sec(x) is -1 at x = \pi, 3\pi, 5\pi, ...

    (a) Now let's suppose that the function to give the graph is of the form y = a\sec(bx+c)

    Using (3) above, the minimum positive value of y is a. So, from the graph, a = 3.

    The first of these is when x = \frac{\pi}{4}. So from (3) again, \frac{b\pi}{4}+ c = 0

    The next is when x = \frac{3\pi}{4}. So \frac{3b\pi}{4}+ c = 2\pi

    Subtracting these two equations, we get \Big(\frac{3b\pi}{4} +c\Big) - \Big( \frac{b\pi}{4}+ c\Big) = 2\pi - 0

    \Rightarrow \frac{2b\pi}{4}=2\pi

    \Rightarrow b =4

    \Rightarrow c = -\pi

    So the function is y = 3\sec(4x-\pi)

    (b) Now start with the fact that \csc(x) = \frac{1}{\sin(x)} and see if you can work out similar statements to numbers (1) - (3) above. Then set up the function y = a\csc(bx+c) and work out the values of a, b, c in the same way.

    Grandad
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  3. #3
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    Wow thanks!! I understand it all now!! I really appreciate it Grandad, you're the best!!

    If only textbooks were written the way you did it, nobody would ever have these problems!
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