3U Maths Question Thread

[anotherworld2b]

I was wondering if someone could explain the rules to antidifferentiate and differentiate trigonometric functions. I don't understand the rules and was wondering if someone knows a good guide or site to use.

[jamonwindeyer]

I was wondering if someone could explain the rules to antidifferentiate and differentiate trigonometric functions. I don't understand the rules and was wondering if someone knows a good guide or site to use.

I wrote this guide a while ago which has the basic rules, otherwise the rules are:



Then those rules work in reverse for integrals:



You'll just be applying these rules, perhaps in conjunction with the product, quotient and/or chain rules - Feel free to give us a specific example of something you are having trouble with!

[itssona]

Heeey

Not having luck with this (seems easy and like it should cancel out but idk)

Underroot (4+cos2x/1-cos2x)

The whole thing is in a surd basically

Is it equivalent to:
2cot(x)
2cot^2(x)
2tan(x)
2tan^2(x)

Thank you

Mod Edit: Post merge

[jamonwindeyer]

Heeey

Not having luck with this (seems easy and like it should cancel out but idk)

Underroot (4+cos2x/1-cos2x)

The whole thing is in a surd basically

Thank you

Hey! Did a quick check in Wolfram and it doesn't look like that expression simplifies very nicely - And it doesn't look like it is equal to any of those options you provided - Where's this from?

[itssona]

Hey! Did a quick check in Wolfram and it doesn't look like that expression simplifies very nicely - And it doesn't look like it is equal to any of those options you provided - Where's this from?

Hmm

Its from my school's extension 1 prelim yearly paper

The answer is : 2cotx

Like I tried factorising and taking the (1-cos2x) out and used the cos (2x) formula but it all just cancels out to 2? As you said it seems like none of them xD

Should i hope this isnt asked in this year's yearly ahaha

[jamonwindeyer]

Hmm

Its from my school's extension 1 prelim yearly paper

The answer is : 2cotx

Like I tried factorising and taking the (1-cos2x) out and used the cos (2x) formula but it all just cancels out to 2? As you said it seems like none of them xD

Should i hope this isnt asked in this year's yearly ahaha

Yeah it definitely isn't \(2\cot{x}\) - You can sketch them both to deduce that. Even substitute \(x=\frac{\pi}{6}\), they give different values so not sure what the go is there!

Do be prepared to handle trig simplifications like this - This is a tough one, and it's made tougher by the fact that it isn't correct

[itssona]

Yeah it definitely isn't \(2\cot{x}\) - You can sketch them both to deduce that. Even substitute \(x=\frac{\pi}{6}\), they give different values so not sure what the go is there!

Do be prepared to handle trig simplifications like this - This is a tough one, and it's made tougher by the fact that it isn't correct

Thank you for showing the sketches ^

Argh you're right!! I'll make sure to be prepared for all sorts of things like this lmaoo! Thanks for confirming that there aren't solutions

[RuiAce]

[itssona]

Wait really?? How
It doesnt seem right when you sub in from what i got
Pleasee explain that

[RuiAce]

[jamonwindeyer]

Wait really?? How
It doesnt seem right when you sub in from what i got
Pleasee explain that

Catch that Rui added the 4 to the start of that cosine function to get the result - Is that what your paper had or?

[itssona]

Catch that Rui added the 4 to the start of that cosine function to get the result - Is that what your paper had or?

Our paper didn't have that buuut I asked my teacher who said that there seems like it's a mistake, and she said there should be a 4

How unprofessional xD

[itssona]

Thank you Rui!

[anotherworld2b]

thank you for your help

I wrote this guide a while ago which has the basic rules, otherwise the rules are:



Then those rules work in reverse for integrals:



You'll just be applying these rules, perhaps in conjunction with the product, quotient and/or chain rules - Feel free to give us a specific example of something you are having trouble with!

[itssona]

heey whats the proper way to graph P(x) = (x-2)(x+2)^2 (3-2x)

like its positive so we start on the bottom right but now what? thank you