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Math Help - pre-calc problem involving trig

  1. #1
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    pre-calc problem involving trig

    I need to determine the domain of each function.

    If you answer can you tell me how you did it?

    h(x) = \frac{1}{1-sin(x)}

    Thanks.
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  2. #2
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    \sin{x} \neq 1 ... why?

    so... x \neq \, ?
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  3. #3
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    Quote Originally Posted by skeeter View Post
    \sin{x} \neq 1 ... why?

    so... x \neq \, ?
    I'm sorry but I don't see how you got \sin{x} \neq 1

    Not saying it's wrong, but can someone tell me how he got that?
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  4. #4
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    look at the denominator ...

    are you familiar with the rule that says division by 0 is undefined?

    if sin{x} = 1, what would be the value of the denominator?

    so ... what does that tell you \sin{x} cannot be equal to ?

    domain is the set of all x-values that can be input into a function without breaking certain rules ... division by 0 is one of those rules that cannot be broken.
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  5. #5
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    Quote Originally Posted by skeeter View Post
    look at the denominator ...

    are you familiar with the rule that says division by 0 is undefined?

    if sin{x} = 1, what would be the value of the denominator?

    so ... what does that tell you \sin{x} cannot be equal to ?

    domain is the set of all x-values that can be input into a function without breaking certain rules ... division by 0 is one of those rules that cannot be broken.
    Yes I am familiar with that rule. I can see the answer being x \neq 1 in an equation that looks like this:

    h(x) = \frac{1}{1-x}

    but if I plug 1 in for x on my problem below, the denominator looks like this:

    h(x) = \frac{1}{1-sin(1)} = \frac{1}{1-0.84147...}

    because sin(1) = 0.84147...

    Am I missing something?
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  6. #6
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    Quote Originally Posted by DHS1 View Post
    Am I missing something?
    Look again. There's a big difference between the statement x \neq 1 and \sin x \neq 1
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  7. #7
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    Quote Originally Posted by Professor Fate View Post
    Look again. There's a big difference between the statement x \neq 1 and \sin x \neq 1
    Wow I can't believe I missed that... haha!

    You, sir, have been thanked. (you too skeeter! especially you!)
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