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Math Help - Domain & range of trig function

  1. #1
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    Domain & range of trig function

    need some help with this one guys..

    y=2sin(3x + pi) -1
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  2. #2
    MHF Contributor red_dog's Avatar
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    First of all use the formula \sin(\pi+x)=-\sin x.

    Then y=-2\sin 3x-1

    The domain is \mathbb{R}.

    We have -1\leq\sin 3x\leq 1\Rightarrow -2\leq -2\sin 3x\leq 2\Rightarrow -3\leq -2\sin 3x-1\leq 1

    So the range is [-3,1]
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  3. #3
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    thanks a lot bro, btw, does the R in the domain mean all rea numbers?
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  4. #4
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    You got it. The fancy "R" does, indeed, mean The Real Numbers. Guess what a fancy "N" means?
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