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Math Help - Find where the two graphs intersect.

  1. #1
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    Find where the two graphs intersect.

    Hello. I'm currently having problems on trying to find the intersection point of these two trig graphs:

    a(t) = -175cos(0.23t) - 75

    b(t) = 172sin(0.23t) - 80


    0 ≤ t ≤ 30

    -----

    Well, I assume this would be the first step:

    -175cos(0.23t) - 75 = 172sin(0.23t) - 80

    Now, I am finding it difficult to do the rest.

    Looks like simple algebra to get the t by itself but it's proving to be harder than I anticipated.

    I know the answers (using my graphics calculator to find the points) and they are:

    (10.12,45.1) and (23.95,-200.19)

    Any help is of course, appreciated.

    Thankyou.
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by sqleung View Post
    Hello. I'm currently having problems on trying to find the intersection point of these two trig graphs:

    a(t) = -175cos(0.23t) - 75

    b(t) = 172sin(0.23t) - 80

    0 ≤ t ≤ 30

    -----

    Well, I assume this would be the first step:

    -175cos(0.23t) - 75 = 172sin(0.23t) - 80

    Now, I am finding it difficult to do the rest.

    Looks like simple algebra to get the t by itself but it's proving to be harder than I anticipated.

    I know the answers (using my graphics calculator to find the points) and they are:

    (10.12,45.1) and (23.95,-200.19)

    Any help is of course, appreciated.

    Thankyou.
    This is not able to be answered by conventional methods


    Try the Newton-Raphson method

    Newton's Method -- from Wolfram MathWorld
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  3. #3
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    Quote Originally Posted by sqleung View Post
    Hello. I'm currently having problems on trying to find the intersection point of these two trig graphs:

    a(t) = -175cos(0.23t) - 75

    b(t) = 172sin(0.23t) - 80

    0 ≤ t ≤ 30

    -----

    Well, I assume this would be the first step:

    -175cos(0.23t) - 75 = 172sin(0.23t) - 80

    Now, I am finding it difficult to do the rest.

    Looks like simple algebra to get the t by itself but it's proving to be harder than I anticipated.

    I know the answers (using my graphics calculator to find the points) and they are:

    (10.12,45.1) and (23.95,-200.19)

    Any help is of course, appreciated.

    Thankyou.
    There are various ways of getting an exact answer (in the sense of writing the answer in the form t = arcsin(number), say). But before time is spent showing this, the question I'd like answered is the following:

    Is an exact answer really required?
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  4. #4
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    Guess that explains the reason why I couldn't get the answer. Newton's method is a little complex for me so I'll stick to technology.

    Thankyou very much for your help.
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  5. #5
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    Quote Originally Posted by mr fantastic View Post
    There are various ways of getting an exact answer (in the sense of writing the answer in the form t = arcsin(number), say). But before time is spent showing this, the question I'd like answered is the following:

    Is an exact answer really required?
    No, the exact answer isn't required.
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