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En

  • one year ago

HELP! please prove that Arctan(-x)= - Arctanx

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  1. zepdrix
    • one year ago
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    I'd prolly just do the same thing as the last one :o\[\large\rm y=-\arctan(x)\]\[\large\rm -y=\arctan(x)\]\[\large\rm \tan(-y)=x\]Since tangent is an odd function,\[\large\rm \tan(-y)=-\tan(y)=x\]\[\large\rm \tan(y)=-x\]\[\large\rm y=\arctan(-x)\]

  2. zepdrix
    • one year ago
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    Lot of weird little steps in that though :D

  3. En
    • one year ago
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    thanks :)))

  4. En
    • one year ago
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    @zepdrix what do you mean to that the tangent is an odd function?

  5. zepdrix
    • one year ago
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    An odd function satisfies this property:\[\large\rm f(-x)=-f(x)\]Examples:\[\large\rm f(x)=x^3\]\[\large\rm f(-x)=(-x)^3=-(x)^3=-f(x)\] \[\large\rm g(x)=\sin(x)\]\[\large\rm g(-x)=\sin(-x)=-\sin(x)=-g(x)\] An even function satisfies this property:\[\large\rm f(-x)=f(x)\]Examples:\[\large\rm f(x)=x^2\]\[\large\rm f(-x)=(-x)^2=(x)^2=f(x)\] \[\large\rm g(x)=\cos (x)\]\[\large\rm g(-x)=\cos(-x)=\cos(x)=g(x)\]

  6. zepdrix
    • one year ago
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    Tangent is like sine in this respect.

  7. zepdrix
    • one year ago
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    It's good to have an understanding of even and odd functions, but at the very least make sure you understand the basics that it allows us with trig functions: `if you have a negative in your cosine, it can disappear` `if you have a negative in your sine or tangent, it can come outside`

  8. En
    • one year ago
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    oh my goodness.. thank you so much

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