HSC 2013 Maths Marathon (archive) (1 Viewer)

RealiseNothing · Oct 16, 2013

Re: HSC 2013 2U Marathon

Menomaths said:
So confused...Who to listen to =.=
Moey's out of the question so it leaves with realizenothing and sai =/

jkjk moey i can see you're good at maths (relative to me at least)

it's 1/e

mahmoudali · Oct 16, 2013

Re: HSC 2013 2U Marathon

Menomaths said:
So confused...Who to listen to =.=
Moey's out of the question so it leaves with realizenothing and sai =/

jkjk moey i can see you're good at maths (relative to me at least)

dont listen to sia he sucks at maths :$

mahmoudali · Oct 16, 2013

Re: HSC 2013 2U Marathon

RealiseNothing said:
it's 1/e

is your avatar a duck or an old guy with a cap i cant tell and its fucking with my mind

Shazer2 · Oct 16, 2013

Re: HSC 2013 2U Marathon

I think he was thinking ln(-1).

Menomaths · Oct 16, 2013

Re: HSC 2013 2U Marathon

mahmoudali said:
is your avatar a duck or an old guy with a cap i cant tell and its fucking with my mind

It's an old man doing the duckface

Sy123 · Oct 16, 2013

Re: HSC 2013 2U Marathon

$Evaluate$

$\sin^2 1^{\circ} + \sin^2 2^{\circ} + \sin^2 3^{\circ} + \dots + \sin^2 88^{\circ} + \sin^2 89^{\circ} + \sin^2 90^{\circ}$

mahmoudali · Oct 16, 2013

Re: HSC 2013 2U Marathon

Sy123 said:
$Evaluate$

$\sin^2 1^{\circ} + \sin^2 2^{\circ} + \sin^2 3^{\circ} + \dots + \sin^2 88^{\circ} + \sin^2 89^{\circ} + \sin^2 90^{\circ}$

$\sin^2 1^{\circ}+ \sin^2 89^{\circ} =1 + .... +\sin^2 44^{\circ}+ \sin^2 46^{\circ}= 44 $your left with$ \ \ sin^2 45^{\circ}+ \sin^2 90^{\circ}= 1+\frac{1}{2}} therefore \ \ 44 + 1+\frac{1}{2}= 45 + \frac{1}{2}}$

Edit: $sin^2 45^{\circ} \ \ is\ \ \frac{1}{2}\ \ $so its 45$\ \ \frac{1}{2}$

integral95 · Oct 16, 2013

Re: HSC 2013 2U Marathon

Sy123 said:
$Evaluate$

$\sin^2 1^{\circ} + \sin^2 2^{\circ} + \sin^2 3^{\circ} + \dots + \sin^2 88^{\circ} + \sin^2 89^{\circ} + \sin^2 90^{\circ}$

is it 95/2?

EDIT: whoops miscounted is it 91/2

Sy123 · Oct 16, 2013

Re: HSC 2013 2U Marathon

mahmoudali said:
$\sin^2 1^{\circ}+ \sin^2 89^{\circ} =1 .... \sin^2 44^{\circ}+ \sin^2 46^{\circ}= 44 $your left with$ \ \ sin^2 45^{\circ}+ \sin^2 90^{\circ}= 1+\frac{1}{\sqrt{2}} therefore \ \ 44 + 1+\frac{1}{\sqrt{2}}= 45 + \frac{1}{\sqrt{2}}$

what

MethewYan said:
is it 95/2?

EDIT: whoops miscounted is it 91/2

yep 91/2

mahmoudali · Oct 16, 2013

Re: HSC 2013 2U Marathon

$prove: \frac{cos(2x)}{cos(x)} = \frac{1-tan^2(x)}{sec(x)}$

ColdLipstick · Oct 16, 2013

Re: HSC 2013 2U Marathon

First 2U Q I made.

EDIT: The Q means Tangent at that x-value for any clarification issues.

RealiseNothing · Oct 16, 2013

Re: HSC 2013 2U Marathon

ColdLipstick said:
First 2U Q I made.

EDIT: The Q means Tangent at that x-value for any clarification issues.

You can do this really easily using a 3U method.

Edit: It's not even a 3U method... my bad.

Will post if no one does.

nakruf · Oct 16, 2013

Re: HSC 2013 2U Marathon

mahmoudali said:
$prove: \frac{cos(2x)}{cos(x)} = \frac{1-tan^2(x)}{sec(x)}$

mate this is 3u.........

anthony_wheels · Oct 16, 2013

Re: HSC 2013 2U Marathon

Sy123 said:
$i) Show that$

$\frac{1-\cos^4 x}{\sin x \cos x + \cot x \cos^4 x} = \frac{\tan x \sec^2 x - \sin x \cos x}{\tan^2 x + \cos^2 x}$

$ii) Hence find$

$\int_0^{\pi/4} \frac{1-\cos^4x}{\sin x \cos x + \cot x \cos^4 x } \ dx$

Yeah?

Sy123 · Oct 16, 2013

Re: HSC 2013 2U Marathon

anthony_wheels said:
View attachment 28790 Yeah?

yep welld one

SpiralFlex · Oct 16, 2013

Re: HSC 2013 2U Marathon

ColdLipstick said:
First 2U Q I made.

EDIT: The Q means Tangent at that x-value for any clarification issues.

$a,b,c\; $must have constraints or the proposition may not hold$$

RealiseNothing · Oct 16, 2013

Re: HSC 2013 2U Marathon

SpiralFlex said:
$a,b,c\; $must have constraints or the proposition will not hold$$

How so? It worked fine for me.

RealiseNothing · Oct 16, 2013

Re: HSC 2013 2U Marathon

The only thing I can think of is stating that $c \neq 0$ if $b=0$

SpiralFlex · Oct 16, 2013

Re: HSC 2013 2U Marathon

Actually, no constaint is needed because of the if-then clause. My mistake.

Carrotsticks · Oct 16, 2013

Re: HSC 2013 2U Marathon

ColdLipstick said:
First 2U Q I made.

EDIT: The Q means Tangent at that x-value for any clarification issues.

I like this question. Seems like the kind of thing I would write.

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