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Math Help - Find Exact Value

  1. #1
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    Find Exact Value

    Let t = theta for short

    If f(t) = csc (t) and f(a) = 2, find the exact value of:

    (A) f(-a)

    (B) f(a) + f(a + 2pi) + f(a + 4pi)
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  2. #2
    Moo
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    Hello,
    Quote Originally Posted by magentarita View Post
    Let t = theta for short

    If f(t) = csc (t) and f(a) = 2, find the exact value of:

    (A) f(-a)

    (B) f(a) + f(a + 2pi) + f(a + 4pi)
    csc(t)=1/sin(t)

    We know that sin(-t)=-sin(t) (you can check in on an unit circle)
    And the sine function is periodic, that is sin(t+2k*pi)=sin(t), where k is any integer.
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  3. #3
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    no...

    Quote Originally Posted by Moo View Post
    Hello,

    csc(t)=1/sin(t)

    We know that sin(-t)=-sin(t) (you can check in on an unit circle)
    And the sine function is periodic, that is sin(t+2k*pi)=sin(t), where k is any integer.
    This is not a matter of knowing the periodic functions.

    This is just plugging and chugging but I have no idea how to break it down.
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  4. #4
    Moo
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    Quote Originally Posted by magentarita View Post
    This is not a matter of knowing the periodic functions.

    This is just plugging and chugging but I have no idea how to break it down.
    Why don't you try ?
    I'm telling you that the sine function is periodic. That is to say, for example, \sin(t+2 \pi)=\sin(t).
    Thus \csc(t+2 \pi)=\csc(t). This helps for question B.
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  5. #5
    Senior Member nikhil's Avatar
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    Check this out

    Quote Originally Posted by magentarita View Post
    Let t = theta for short

    If f(t) = csc (t) and f(a) = 2, find the exact value of:

    (A) f(-a)

    (B) f(a) + f(a + 2pi) + f(a + 4pi)
    f(t)=csc(t)
    f(a)=csc(a)=2
    so f(-a)=csc(-a)=-csc(a)=-2 (as csc(a)=2 )
    2) f(a) + f(a + 2pi) + f(a + 4pi)
    =csc(a)+csc(a+2pi)+csc(a+4pi)
    =csc(a)+csc(a)+csc(a)
    (csc(t+2n pi) where n is a integer =csc(t))
    =2+2+2=6 hence
    f(a) + f(a + 2pi) + f(a + 4pi)=6
    hope this helps
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  6. #6
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    Thanks

    Quote Originally Posted by magentarita View Post
    This is not a matter of knowing the periodic functions.

    This is just plugging and chugging but I have no idea how to break it down.
    Quote Originally Posted by nikhil View Post
    f(t)=csc(t)
    f(a)=csc(a)=2
    so f(-a)=csc(-a)=-csc(a)=-2 (as csc(a)=2 )
    2) f(a) + f(a + 2pi) + f(a + 4pi)
    =csc(a)+csc(a+2pi)+csc(a+4pi)
    =csc(a)+csc(a)+csc(a)
    (csc(t+2n pi) where n is a integer =csc(t))
    =2+2+2=6 hence
    f(a) + f(a + 2pi) + f(a + 4pi)=6
    hope this helps
    Excellent reply. Thanks!
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