Answering a maths question with something not on the course?

Chuchoter

I'm finally after figuring out how to differentiate inverse trigonometric functions but its using sec^2 which isn't technically on our course. Its the triangle method you use for sin^-1 and Cos^-1 but the differentiate of tan^-1 is sec^2. Its correct, its still differentiation, but would it not be counted?

finality

But the derivative of tan inverse isn't sec^2, that's the derivative of tan. Or am I misunderstanding?

I still don't see why you wouldn't just use the derivative given in the tables, it's as easy as just writing it down.

ChemHickey

It is on our course is it not? You can then say sec^2 = 1-tan^2 or 1/cos^2 (( I hope those are right! I think they are!?!))

But as finality said, it is as easy to do the formula, unless it is very awkward! I do use the sec^2 one really often though!!

finality

What is the sec^2 one? how can you use it for tan inverse?

FaoiSin

Oh jaysus. This is like a different language. If there's something in Maths thats not in the log tables I'm fecked

ChemHickey

finality wrote: »

What is the sec^2 one? how can you use it for tan inverse?

Implicit differentiation! If y=tan-1x then tany=x then sec^2dy/dx=1 then dy/dx = 1/sec^2 x and then dy/dx is cos^2 x..... I THINK! I'm not sure of my differentials... they're from my head!

jumpguy

As long as you come to the correct conclusion in a clearly shown, logically correct manner then you should get all your marks.

deathbythelc

I wanna puke everywhere reading all of this.

But, yes, if what you're saying works and isn't on the course you are still able to use it. As long as you show your work and answer the question then you can't be docked marks.

Wesc.

Wait I think my get what your on about here, would an example of this be like the 2008 Q7 part c? I'm not sure if we're on the same wavelength here but just in case!
Is it where you draw out a triangle and get a value for tan^inverse instead of cos or sin inverse, by using pythagras theorem? As in,say you have sin( some fraction ) you plot that on a triangle as opposite over hypoteneuse to get the adjacent side? And then get the tan inverse of the opposite over adjacent? If this is what you mean, then you still have to apply the tan inverse formula, the differential is not sec^2!

ChemHickey

Wesc. wrote: »

Wait I think my get what your on about here, would an example of this be like the 2008 Q7 part c? I'm not sure if we're on the same wavelength here but just in case!
Is it where you draw out a triangle and get a value for tan^inverse instead of cos or sin inverse, by using pythagras theorem? As in,say you have sin( some fraction ) you plot that on a triangle as opposite over hypoteneuse to get the adjacent side? And then get the tan inverse of the opposite over adjacent? If this is what you mean, then you still have to apply the tan inverse formula, the differential is not sec^2!

No but it's when you have a crazy piece to differentiate eg y=tan-1(rootx^6/5x -9x^8) or something and you really are not bothered to do the formula, you write it as tany=(whatever i said there^) and then differentiate implicitly

finality

ChemHickey wrote: »

Implicit differentiation! If y=tan-1x then tany=x then sec^2dy/dx=1 then dy/dx = 1/sec^2 x and then dy/dx is cos^2 x..... I THINK! I'm not sure of my differentials... they're from my head!

Oh of course. Wouldn't it be
sec^2(y)dy/dx = 1
though? I tend to get confused when doing it that way :L


But anyway, yeah it's fine to use implicit differentiation OP, pretty sure it is on the course - it generally gives that method in marking schemes too iirc.

ChemHickey

finality wrote: »

ChemHickey wrote: »

Implicit differentiation! If y=tan-1x then tany=x then sec^2dy/dx=1 then dy/dx = 1/sec^2 x and then dy/dx is cos^2 x..... I THINK! I'm not sure of my differentials... they're from my head!

Oh of course. Wouldn't it be
sec^2(y)dy/dx = 1
though? I tend to get confused when doing it that way :L


But anyway, yeah it's fine to use implicit differentiation OP, pretty sure it is on the course - it generally gives that method in marking schemes too iirc.

Haha ya sorry- I'm on my phone. x is pretty much y on this!

to be honest, i prefer implicit anyway! easier and works everytime.

I <3 calculus

Not as fond on integration though. It's easy but just tiresome!

Chuchoter

Actually you're completely right the differential of TAN is sec^2 not tan^1, but that was a typo!

Anyway it seems like I can do what I'm trying to do. I know there is another way but for hard ones I always get it wrong so this way works better for me!

Zaffy

If it works, then it's fine.