- #1
nicksbyman
- 19
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Hey guys these aren't math exercises; I just don't understand a couple parts in my textbook.
1. Cos(x)/Sin(x) = Cot(x), but Cot(x) * sin(x) ≠ cos(x). Why?
I know tan(x) * sin(x) ≠ cos(x) because during precalculus nobody ever used sin(x) * cot(x) = cos(x) for anything, but I don't know why you can't do this operation. I think it might have something to do with a 0 in a denominator?
2. This is a harder question I think. In one section of my book the derivatives of trig functions are defined like this:
d/dx [sinx] = cos(x)
d/dx [tanx] = secˆ2(x)
etc...
BUT, a couple sections later in the textbook when the chain rule is introduced the definitions of the derivatives of the trig functions change:
d/dx [sinx] = cos(x)* x'
d/dx [tanx] = secˆ2(x) * x'
d/dx [secx] = sec(x)tan(x) * x'
etc...
Explain please :)
Thanks
1. Cos(x)/Sin(x) = Cot(x), but Cot(x) * sin(x) ≠ cos(x). Why?
I know tan(x) * sin(x) ≠ cos(x) because during precalculus nobody ever used sin(x) * cot(x) = cos(x) for anything, but I don't know why you can't do this operation. I think it might have something to do with a 0 in a denominator?
2. This is a harder question I think. In one section of my book the derivatives of trig functions are defined like this:
d/dx [sinx] = cos(x)
d/dx [tanx] = secˆ2(x)
etc...
BUT, a couple sections later in the textbook when the chain rule is introduced the definitions of the derivatives of the trig functions change:
d/dx [sinx] = cos(x)* x'
d/dx [tanx] = secˆ2(x) * x'
d/dx [secx] = sec(x)tan(x) * x'
etc...
Explain please :)
Thanks
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