HSC Mathematics Marathon (1 Viewer)

[Drongoski]

New question:

Show
(sinx+sin3x+sin5x+sin7x+sin9x)/(cosx+cos3x+cos5x+cos7x+cos9x) = tan5x

LHS

 

[ohexploitable]

Drongoski, are those identities in the HSC course?

I'm talking about,

etc.

 

[ninetypercent]

^ yes and no. typical exam questions will have part (i) to show the identity and then in part (ii) you use it

 

[ohexploitable]

Anyway, new question:

"hscishard" and "bored of fail", you're not allowed to answer this

 

[hscishard]

Lol. Good luck to whoever attempts that question ^

 

[4025808]

Drongoski, are those identities in the HSC course?

I'm talking about,

etc.

it used to be in the syllabus but they took it off...
nevertheless it's still useful to learn esp in trig expansion

 

[Drongoski]

^ yes and no. typical exam questions will have part (i) to show the identity and then in part (ii) you use it

Yes = not directly. But if I were doing Ext 2 I will try to add it to my arsenal. Useful in some of the messier derivations in conics (see P89, Cambridge 4U book)

 

[jyu]

New question:

Show
(sinx+sin3x+sin5x+sin7x+sin9x)/(cosx+cos3x+cos5x+cos7x+cos9x) = tan5x

This question does not require the use of those formulas.

 

[AAEldar]

Anyway, new question:

"hscishard" and "bored of fail", you're not allowed to answer this

I'll give it a crack. I remember seeing your solution/hscishard's solution (whichever one of you uploaded the handwritten answer) but can't really remember it LOL. Might not end well.

 

[ohexploitable]

I'll give it a crack. I remember seeing your solution/hscishard's solution (whichever one of you uploaded the handwritten answer) but can't really remember it LOL. Might not end well.

It was mine

 

[jyu]

Anyway, new question:

"hscishard" and "bored of fail", you're not allowed to answer this

 

[Trebla]

Find

 

[jyu]

Find

Factorise: 1-(sinx)^10=(1-(sinx)^2)(1+(sinx)^2+(sinx)^4+(sinx)^6+(sinx)^8)
=(cosx)^2 (1+(sinx)^2+(sinx)^4+(sinx)^6+(sinx)^8)

integ (cosx)(1+(sinx)^2+(sinx)^4+(sinx)^6+(sinx)^8) dx

let u=sinx etc.

integ (1+u^2+u^4+u^6+u^8) du etc.

 

[Trebla]

Nice work...though I was hoping someone would pick it up more in the lines of a geometric series

 

[hscishard]

Why are uni students dominating this thread?

 

[ohexploitable]

Why are uni students dominating this thread?

I've noticed that too...

 

[Drongoski]

Nice work...though I was hoping someone would pick it up more in the lines of a geometric series

Trebla

Interesting question & beautiful solution. I thought I knew how to integrate. Ends up similar to jyu's.

 

[UnrealAnchovies]

Find

What's the likelihood of that appearing in the 4U HSC exam?

 

[cutemouse]

What's the likelihood of that appearing in the 4U HSC exam?

Probably like 15% I'd say...

 

[jyu]

very likely with a hinting question beforehand