Induction Involving Trigonometric Terms (1 Viewer)

[ssglain]

A friend of mine recently showed me some questions she got from her tutoring college on proof by mathematical induction that involved trigonometric terms. I've never seen this type of questions before in any of my text books (Cambridge & Margret Grove, both Yrs 11 & 12) but according to my friend they are questions from previous HSC exams. I don't think I'd like to walk into my exam some eight months down the track to be faced with question types that I have no experience with. Does anyone know of text books that teach this type of questions?

 

[pLuvia]

Fitzpatrick might have some, don't really remember. But just look at past HSC questions they are sure to have some.

They're not hard at all, follows all the same concepts and procedures just requires some manipulation and use of the double angle and half angle formulae

 

[haque]

try some of the 4u induction and look at the 3u paper from last year-it had one-but the trig ones are much easier than they may look-it's all a psychological thing.

 

[ssglain]

Thanks for the suggestions. I'll try Fitzpat and those 4U ones. I've just looked through the past Ext-1 papers from 1994-2003 but I couldn't find any - I must be going blind or something..

haque: I'm very envious of your Bsc(Adv)/MBBS at USyd. Congrats, mate.

 

[haque]

thank u ssqlain(quite a few bosers from 06 r doing med)-in regards to the trig thing- most of them are variations of sumd to products and products to sum type q-u can try the 1972 3u hsc(It sounds ridiculous but u can get it from the bos resources i think) q 7 i think it was-in those days 3u had 10 q. the 4u trials are an ideal place for trig induction q-but again, i don't think u'll find it too difficult-their notation just makes them look bigger than they are. IMO the induction q related to permuations and that r probably the harder ones.

 

[jyu]

A friend of mine recently showed me some questions she got from her tutoring college on proof by mathematical induction that involved trigonometric terms. I've never seen this type of questions before in any of my text books (Cambridge & Margret Grove, both Yrs 11 & 12) but according to my friend they are questions from previous HSC exams. I don't think I'd like to walk into my exam some eight months down the track to be faced with question types that I have no experience with. Does anyone know of text books that teach this type of questions?

Here is one from a textbook.

Given sin x not = 0, and n is a natural number, prove that

cos(x) cos(2x) cos(3x) ...... cos((2^(n-1))x) = (sin((2^n)x))/((2^n)sin(x)).

 

[ssglain]

Here is one from a textbook.

Given sin x not = 0, and n is a natural number, prove that

cos(x) cos(2x) cos(3x) ...... cos((2^(n-1))x) = (sin((2^n)x))/((2^n)sin(x)).

Thanks a lot for that.

Just one thing though: cos(x) cos(2x) cos(3x) ...... cos((2^(n-1))x)

By the expression for the nth term, shouldn't the third term be cos(4x)? Or was that a typo so the nth term is cos((2*(n-1))x)? I'll give both cases a try.

[Edit] Oh wait, but if the nth term is cos((2*(n-1))x) then at n=1, LHS=1 which doesn't equal RHS. So was cos(3x) the typo and should be cos(4x) or am I missing something here?

[Edit 2] Never mind, I just worked it out. cos((2^(n-1))x) as the nth term is right. That question was a lot easier than I thought. I sure hope they're all like this. Thank you again jyu for the question.

 

[ssglain]

thank u ssqlain(quite a few bosers from 06 r doing med)-in regards to the trig thing- most of them are variations of sumd to products and products to sum type q-u can try the 1972 3u hsc(It sounds ridiculous but u can get it from the bos resources i think) q 7 i think it was-in those days 3u had 10 q. the 4u trials are an ideal place for trig induction q-but again, i don't think u'll find it too difficult-their notation just makes them look bigger than they are. IMO the induction q related to permuations and that r probably the harder ones.

I've just recently started participating in the student community (.. perhaps not so good a thing for my HSC) so you're the first I've noticed. I do have my eye on that course and hopefully I will do well enough to score an interview for it.

Again, thank you for the suggestions. I will surely look into them.

 

[haque]

ssqlain i wasn't being critical or anything if that's what u thought(I was merely commenting, because i hadn't seen so many people do med before on the forums)-if i were u i would have joined bos later-u might waste too much time lol. Get some uni textbooks as well and do some q related to 3u from there(ther are overlaps adnthey ask harder q related to calculus). Cambridge is best though.

 

[ssglain]

ssqlain i wasn't being critical or anything if that's what u thought(I was merely commenting, because i hadn't seen so many people do med before on the forums)-if i were u i would have joined bos later-u might waste too much time lol. Get some uni textbooks as well and do some q related to 3u from there(ther are overlaps adnthey ask harder q related to calculus). Cambridge is best though.

I thought nothing of the sort, and to be honest I'm a bit puzzled as to which phrase I was supposed to have mistaken for being critical. Hehe.

Lol. You're right. I might end up wasting too much time here. I should probably erm.. turn my computer off right now. Yeah.. But I do agree, Cambridge is best.