Prelim 2016 Maths Help Thread (1 Viewer)

[integral95]

yeah I know but which is the best to take?

The rule of thumb is when you have 1-cos(2x) you end up with 2sin^2(x)
And 1+cos(2x) gives 2cos^2(x)

You'll nee those identities when you learn to integrate sin^2(x) as well in the future.

Otherwise when you have cos(2x) by itself there is no rule of thumb. There's more intuition required for those. e.g. difference of two squares may mean I leave it in the original form cos^2(x)-sin^2(x)

essentially the identity to remove the value 1.

 

[eyeseeyou]

cos4x=8cos^4x-8cos^2x+1

 

[leehuan]

essentially the identity to remove the value 1.

Obviously you don't always get that e.g. 2-cos(2x)

 

[leehuan]

cos4x=8cos^4x-8cos^2x+1

cos(4x)
=1-2cos^2(2x)
=1-2[cos(2x)]^2
=1-2[1-2cos^2(x)]^2

Expand it all out

 

[eyeseeyou]

cos(4x)
=1-2cos^2(2x)
=1-2[cos(2x)]^2
=1-2[1-2cos^2(x)]^2

Expand it all out

In this case don't I have to use double angle formula?

 

[leehuan]

In this case don't I have to use double angle formula?

I literally used the double angle formula twice

 

[eyeseeyou]

I literally used the double angle formula twice

LHS or RHS?

 

[leehuan]

LHS or RHS?

Are you serious...

What do you think?
I started on cos(4x) is that LHS or RHS

cos(4x) = 1 - 2 cos^2(2x) by double angle

And then another double angle to come

 

[eyeseeyou]

Are you serious...

What do you think?
I started on cos(4x) is that LHS or RHS

cos(4x) = 1 - 2 cos^2(2x) by double angle

And then another double angle to come

Oh yeah shit DW leehaun

 

[eyeseeyou]

1.cot(x+y)=(cot x cot y -1)/(cot x + cot y)
2.(tan 2theta-tan theta)/(tan2 theta +cot theta)=tan squared theta
3. (1-tan theta than 2 theta)/(1=tantheta than 2 theta)= 4 cos^2 theta -3

 

[eyeseeyou]

Leehuan, Integrand?

 

[Drongoski]

Are you serious...

What do you think?
I started on cos(4x) is that LHS or RHS

cos(4x) = 1 - 2 cos^2(2x) by double angle

And then another double angle to come

Incorrect.

2cos² 2x = 1 + cos 4x

 

[Drongoski]

 

[integral95]

1.cot(x+y)=(cot x cot y -1)/(cot x + cot y)
2.(tan 2theta-tan theta)/(tan2 theta +cot theta)=tan squared theta
3. (1-tan theta than 2 theta)/(1=tantheta than 2 theta)= 4 cos^2 theta -3

???

for Q 2

you use the double angle formula for both (tan 2theta), then you go through the tedious algebra to simplify to the RHS. (hint multiply top and bottom by (1-tan^2)(tan))

 

[kawaiipotato]

1.cot(x+y)=(cot x cot y -1)/(cot x + cot y)

3. (1-tan theta tan 2 theta)/(1+tantheta tan 2 theta)= 4 cos^2 theta -3

.

 

[leehuan]

Incorrect.

2cos² 2x = 1 + cos 4x

Ugh. Ok never doing maths again whilst on alcohol.


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[eyeseeyou]

Ugh. Ok never doing maths again whilst on alcohol.


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Were you actually...?

 

[Sien]

Were you actually...?

Yep he called some fugly the other night when he was on alcohol

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[Trebla]

Ugh. Ok never doing maths again whilst on alcohol.

Doing a 'simple' but thought heavy maths question is a great test to see how sobered up you are after drinking

 

[eyeseeyou]

Doing a 'simple' but thought heavy maths question is a great test to see how sobered up you are after drinking

Have u done it b4?