Try this one. more calc 2

[Trezza]

Thanks for everyone thats been helping me out but i got one more problem that i am stuck on.

note ~ mean integral sign

~ cos(3x)/sin(2x)dx = -1/2ln| cscx+cotx| + 2cosx +c
I have to prove that is true.
What I know:

sin^2 (x)+cos^2 (x) =1
sin(2x) = 2sin x cos x
cos (3x) = 4 cos^3 (x) - 3 cos (x)

how am i going to csc and cots?

 

[helpme]

Are you sure cos(3x) isn't cos(x)-4sin^2(x) * cos(x)

I was trying to work backwards but I don't end up with the same form as your inital integral. TI-89 won't integrate the inital integral either.

 

[Kyteland]

I got it. Hold on while I type up the explaination.

But first a lecture on doing your own homework....

You really should try to do this kind of thing yourself. The steps to solve this question really weren't all that hard and if you don't learn to do it you will be screwed later on (like on the test...)

Explaination coming...

 

[LordSnailz]

Originally posted by: Kyteland
I got it. Hold on while I type up the explaination.

But first a lecture on doing your own homework....

You really should try to do this kind of thing yourself. It steps to solve this question really weren't all that hard and if you don't learn to do it you will be screwed later on (like on the test...)

Explaination coming...

couldn't agree more, youdon't really learn unless you struggle with it ...

 

[CrazyPerson]

makes my head spin

 

[Trezza]

Originally posted by: helpme
Are you sure cox(3x) isn't cos(x)-4sin^2(x) * cos(x)

cos(x)-4sin^2(x) *3 cos(x) is whats on the paper but it might be a typo

 

[Kyteland]

1) start by substituting you trig identities sin(2x) = 2sin x cos x and cos (3x) = 4 cos^3 (x) - 3 cos (x).
cos(3x)/sin(2x)
= (4 cos^3 (x) - 3 cosx)/( 2 sinx cosx)

2) reduce your fraction (take out a factor of cosx).
(4 cos^3 (x) - 3 cosx)/( 2 sinx cosx)
= (4 cos^2 (x) - 3)/( 2 sinx)

3) convert all sin^2 x to cos^2 x using trig identities
(4 cos^2 (x) - 3)/( 2 sinx)
= (4 (1-sin^2 (x)) - 3)/( 2 sinx)
= (4 - 4sin^2 x - 3) / 2sinx
= (1-4sin^2 x) / 2sinx

4) split the fraction and reduce
(1-4sin^2 x) / 2sinx
= 1/ 2sinx - 4sin^2 x / 2sinx
= cscx/2 - 2sinx

Now you still have to integrate this equation.
1/2*integral(cscx) - 2*integral(sinx)
= 1/2*ln|cscx - cotx| +2*cosx + C

I must have a trivial math mistake somwhere because my answer is slightly different then what you said to prove, but you get the idea.

Edit: Double checked and it seems what I have is right. You have a typo above.

 

[alkemyst]

hehe yeah I remember problems almost identical in my calc 2 class, you could probably find solutions online through google to these textbook problems.

 

[Kyteland]

Originally posted by: Trezza

Originally posted by: helpme
Are you sure cox(3x) isn't cos(x)-4sin^2(x) * cos(x)

cos(x)-4sin^2(x) *3 cos(x) is whats on the paper but it might be a typo

no they are both right

cos(x)-4sin^2(x) *cos(x)
= cos(x)-4*(1-cos^2(x)) *cos(x) <---- apply sin^2x + cos^2 x = 1
= cosx - 4cosx + 4cos^3 x
= 4cos^3 x - 3cosx

they are exactly the same

 

[helpme]

Whoops, I figured they just needed some manipulation. I'm so tired of math, I've already had my 6 quarters of it 😀

 

[Kyteland]

Part of the reason math seems to suck so hard is that too many profs try to focus on the "memorize all this sh!t" style of teaching. That blows something hard. That is not the point of math.

I much preferred the math classes that were open book or allowed a sheet of notes for exams. That way they could test you on you conceptual understanding and not on your ability to memorize an assload of equations and identities. IRL you can look those up from a book.

I also much prefered classes that didn't allow calculators :evil:

 

[Yax]

Interesting. Present your homework as a test or game so that every sucker on the forum will help you out. Then turn in the answers and get the A.

 

[alkemyst]

Originally posted by: Kyteland
Part of the reason math seems to suck so hard is that too many profs try to focus on the "memorize all this sh!t" style of teaching. That blows something hard. That is not the point of math.

I much preferred the math classes that were open book or allowed a sheet of notes for exams. That way they could test you on you conceptual understanding and not on your ability to memorize an assload of equations and identities. IRL you can look those up from a book.

I also much prefered classes that didn't allow calculators :evil:

The thing is at the lower levels memorization is key....if you can't memorize a great deal in chem I - III, Calc I - III, biology/zoology...you will be spending most of your time looking things up in advanced classes.

The truth is in Calc you memorize a lot because you don't have the skills to do the proofs for much of what is taken for granted....even in a higher level class like queueing theory so much would be impossible for the average student to 'prove', so you read and memorize and stick in the numbers.

I believe in using calculators....it's a tool that would be everywhere anyways, I also believe in open book. Of course the problems would have to be harder than the typical 'homework' question, but with an open book even the lamest student should be able to pass.

I favor the index card type test, where book is closed but you can write whatever notes possible on a 4x6 or 3x5 index card.

 

[Trezza]

Originally posted by: cheapbidder01
Interesting. Present your homework as a test or game so that every sucker on the forum will help you out. Then turn in the answers and get the A.

what your not interested in the free flame suit giveaway?

I never turned this into a game or anything like this if you read my first post i clearly state that this is homework and the only thing that people get who help me out is my thanks. You know you really prove your coolness by coming into a thread thats asking for help and being a troll.