HSC 2013 Maths Marathon (archive) (1 Viewer)

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RealiseNothing

what is that?It is Cowpea
Re: HSC 2013 2U Marathon

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

Member
Re: HSC 2013 2U Marathon

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

Member
Re: HSC 2013 2U Marathon

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

Shazer2

Member
Re: HSC 2013 2U Marathon

I think he was thinking ln(-1).

Menomaths

Exaı̸̸̸̸̸̸̸̸lted Member
Re: HSC 2013 2U Marathon

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

This too shall pass
Re: HSC 2013 2U Marathon

$\bg_white Evaluate$

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

mahmoudali

Member
Re: HSC 2013 2U Marathon

$\bg_white Evaluate$

$\bg_white \sin^2 1^{\circ} + \sin^2 2^{\circ} + \sin^2 3^{\circ} + \dots + \sin^2 88^{\circ} + \sin^2 89^{\circ} + \sin^2 90^{\circ}$
$\bg_white \sin^2 1^{\circ}+ \sin^2 89^{\circ} =1 + .... +\sin^2 44^{\circ}+ \sin^2 46^{\circ}= 44 your left with \ \ sin^2 45^{\circ}+ \sin^2 90^{\circ}= 1+\frac{1}{2}} therefore \ \ 44 + 1+\frac{1}{2}= 45 + \frac{1}{2}}$

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

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integral95

Well-Known Member
Re: HSC 2013 2U Marathon

$\bg_white Evaluate$

$\bg_white \sin^2 1^{\circ} + \sin^2 2^{\circ} + \sin^2 3^{\circ} + \dots + \sin^2 88^{\circ} + \sin^2 89^{\circ} + \sin^2 90^{\circ}$
is it 95/2?

EDIT: whoops miscounted is it 91/2

Sy123

This too shall pass
Re: HSC 2013 2U Marathon

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

is it 95/2?

EDIT: whoops miscounted is it 91/2
yep 91/2

mahmoudali

Member
Re: HSC 2013 2U Marathon

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

ColdLipstick

Member
Re: HSC 2013 2U Marathon

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

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RealiseNothing

what is that?It is Cowpea
Re: HSC 2013 2U Marathon

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

New Member
Re: HSC 2013 2U Marathon

$\bg_white prove: \frac{cos(2x)}{cos(x)} = \frac{1-tan^2(x)}{sec(x)}$
mate this is 3u.........

anthony_wheels

Member
Re: HSC 2013 2U Marathon

$\bg_white i) Show that$

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

$\bg_white ii) Hence find$

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

Sy123

This too shall pass
Re: HSC 2013 2U Marathon

yep welld one

SpiralFlex

Well-Known Member
Re: HSC 2013 2U Marathon

EDIT: The Q means Tangent at that x-value for any clarification issues.
$\bg_white a,b,c\; must have constraints or the proposition may not hold$

RealiseNothing

what is that?It is Cowpea
Re: HSC 2013 2U Marathon

$\bg_white a,b,c\; must have constraints or the proposition will not hold$
How so? It worked fine for me.

RealiseNothing

what is that?It is Cowpea
Re: HSC 2013 2U Marathon

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

SpiralFlex

Well-Known Member
Re: HSC 2013 2U Marathon

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

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Carrotsticks

Retired
Re: HSC 2013 2U Marathon