VCE Methods Question Thread!

[pi]

Try this: Multiply both numerator and denom by (1+sin(x)). cos^2(x) will cancel out (remember that cos^2(x) = 1 - sin^2(x)) and leave you with 1+sin(x) and the rest is elementary

[Jenny_2108]

Hey guys, I can't do this

Please help it add to my internal mark if I can get it.

Interal( (cos(x)^2)/(1-sin(x)) dx)

I've tried integration by parts, integration by substitution... EVERYTHING!!

You can do as Vegemite suggested or do this way
cos(x)^2/1-sin(x)= 1- sin(x)^2/1-sin(x)= 1+sin(x)
Then you intergrate it => x-cos(x)

[CommanderElahi]

Thanks VegimitePi, your a legend man.

[sh00my]

Try this: Multiply both numerator and denom by (1+sin(x)). cos^2(x) will cancel out (remember that cos^2(x) = 1 - sin^2(x)) and leave you with 1+sin(x) and the rest is elementary

Thanks man, saved my life.

[sh00my]

Hey guys, I can't do this

Please help it add to my internal mark if I can get it.

Interal( (cos(x)^2)/(1-sin(x)) dx)

I've tried integration by parts, integration by substitution... EVERYTHING!!

You can do as Vegemite suggested or do this way
cos(x)^2/1-sin(x)= 1- sin(x)^2/1-sin(x)= 1+sin(x)
Then you intergrate it => x-cos(x)

Thanks aswell Jenny. Really efficient method

[BoredSatan]

Try this: Multiply both numerator and denom by (1+sin(x)). cos^2(x) will cancel out (remember that cos^2(x) = 1 - sin^2(x)) and leave you with 1+sin(x) and the rest is elementary

I'm not sure you can do this because if sin(x) is -1, then your fraction is undefined. I would follow Jenny's method.

Although it has been a while since I've done math

[soccerboi]

This isn't a difficult question, but i would just like to see how you solve these sort of questions, where it isn't just x inside the bracket.

Solve tan (3x+3pi)=1/root 3 where xE[-pi,pi]

I sometimes adjust the domain incorrectly and get my answers slightly off..
Thanks

[kamil9876]

being in is equivalent to being in , so solve over and then recover the x's

[soccerboi]

Simple question but i forgot:
If pi/3 is the angle in the 1st quadrant, and i want the angle in the 4th quadrant, its 2pi-pi/3 which is 5pi/3. Is taking the minus of the 1st quadrant angle (i.e -pi/3) the same if asked for the 4the quadrant angle? Im pretty sure its not but can someone explain?
Thanks

[Lasercookie]

Simple question but i forgot:
If pi/3 is the angle in the 1st quadrant, and i want the angle in the 4th quadrant, its 2pi-pi/3 which is 5pi/3. Is taking the minus of the 1st quadrant angle (i.e -pi/3) the same if asked for the 4the quadrant angle? Im pretty sure its not but can someone explain?
Thanks

It is the same angle. So one full rotation of the unit circle is . We can add and subtract this period and we'll have the same angle.

So we have: edit: you might also want to think about why we're doing in the first place



You can also think of as rotating around the unit circle in the opposite direction than usual (clockwise)

You might also remember doing this a lot in spesh with the argument of a complex number, since we normally state that with the domain

edit: fixed latex errors

[Lasercookie]

Actually wait, I think I interpreted your question wrongly. Were you asking that if you were asked for the 4th quadrant angle, could you state as your answer? Similar to this:

You might also remember doing this a lot in spesh with the argument of a complex number, since we normally state that with the domain

I think the answer would be "it depends on what domain you're working in".

[soccerboi]

Well, the question was solve cos(3x/2)=1/2 for x E [-pi/2,pi/2].
The first line of the solutions was:
3x/2 = pi/3, -pi/3, 5pi/2

I know the quadrants are 1st and 4th, but confused why they had -pi/3 and also 5pi/3, aren't they both the same angle in the 4th quadrant?

I know i should know this stuff but i just forgot...

[Lasercookie]

Well, the question was solve cos(3x/2)=1/2 for x E [-pi/2,pi/2].
...
I know the quadrants are 1st and 4th, but confused why they had -pi/3 and also 5pi/3, aren't they both the same angle in the 4th quadrant?

Yes, but that domain cuts across more than one period of the cos graph. You're going to get quadrants repeating

[soccerboi]

I'm sorry but could you please elaborate, i'm not quite getting my head around it.

[Bhootnike]

For f : R → R, f (x) =
a Find f (x).  - all good here

i dont get how to do the following:

b Find an approximation for f (h), where h is small, in terms of h and a.
c Find an approximation for f (b + h), where h is small, in terms of b, h and a.