Ken's specialist question thread!

[TrueTears]

Let



Find the value of u for which V(u) is a maximum and find the corresponding theta

[kensan]

Ohh ok, I see the steps but from wouldn't it go to ??
I get the steps now though, ty!



And also this one, from VCAA 2007

  when  , find exact value of

Would I use double angle formula to find just tanx? I'm confused with this one also XD I have a sac tomorrow on trig, stressing hard lol

[TrueTears]

lol yup typo'd, so it'd be a cubic instead of quad

for your new question do this:







Let



Solving the quadratic yields

But since

So

But

Now just solve for and take the answer that satisfies the domain

should be correct if i haven't made any arithmetic errors, but if i did, same steps apply

[yawho]

lol yup typo'd, so it'd be a cubic instead of quad

for your new question do this:







Let



Solving the quadratic yields

But since

So

But

Now just solve for and take the answer that satisfies the domain

should be correct if i haven't made any arithmetic errors, but if i did, same steps apply

would be easier using 1+tan^2=sec^2 to get cos2x=7/9, then sinx=1/3

[TrueTears]

yup that's a good elegant way

[kensan]

Asked teacher today, he said to draw triangle, find cos(2x) then use double angle formula to find sinx.
Also had SAC today.. was so hard, everyone found it so difficult. I could do all the q's in the textbook but the textbook doesn't really have any application questions so that annoys me. SAC questions were so much harder than expected, how can I study topics in more depth? We are using the Heinemann VCE Zone text book, is it a good one?

[rife168]

Asked teacher today, he said to draw triangle, find cos(2x) then use double angle formula to find sinx.
Also had SAC today.. was so hard, everyone found it so difficult. I could do all the q's in the textbook but the textbook doesn't really have any application questions so that annoys me. SAC questions were so much harder than expected, how can I study topics in more depth? We are using the Heinemann VCE Zone text book, is it a good one?

We use Heinemann as well and I agree, the application questions aren't all that good.
I suggest you somehow get a copy of the Essentials textbook, the questions are harder and require a better understanding, thus better prepare you for SACs/exams.

[kensan]

Asked teacher today, he said to draw triangle, find cos(2x) then use double angle formula to find sinx.
Also had SAC today.. was so hard, everyone found it so difficult. I could do all the q's in the textbook but the textbook doesn't really have any application questions so that annoys me. SAC questions were so much harder than expected, how can I study topics in more depth? We are using the Heinemann VCE Zone text book, is it a good one?

We use Heinemann as well and I agree, the application questions aren't all that good.
I suggest you somehow get a copy of the Essentials textbook, the questions are harder and require a better understanding, thus better prepare you for SACs/exams.

Are there even any application questions in Heinemann? I couldn't find any.
Cheers man, yeah I'll try and get a copy

Is it just called 'Essential Specialist Mathematics: Third edition'?

[rife168]

Asked teacher today, he said to draw triangle, find cos(2x) then use double angle formula to find sinx.
Also had SAC today.. was so hard, everyone found it so difficult. I could do all the q's in the textbook but the textbook doesn't really have any application questions so that annoys me. SAC questions were so much harder than expected, how can I study topics in more depth? We are using the Heinemann VCE Zone text book, is it a good one?

We use Heinemann as well and I agree, the application questions aren't all that good.
I suggest you somehow get a copy of the Essentials textbook, the questions are harder and require a better understanding, thus better prepare you for SACs/exams.

Are there even any application questions in Heinemann? I couldn't find any.
Cheers man, yeah I'll try and get a copy

Is it just called 'Essential Specialist Mathematics: Third edition'?

No there are just a few 'extended answer' questions that aren't really all that different to the short answer ones.

Yeah that sounds right, I have the 2nd edition and it is still very helpful.

[Wikipedian]

If I am asked to give a complex number in polar form, and I get an answer like: 2cis(2pi), can the answer be 2, or must it be 2cis(0)?

What if it's 2cis(pi)? Can I answer it as -2, or must it be 2cis(pi)?

[rife168]

If I am asked to give a complex number in polar form, and I get an answer like: 2cis(2pi), can the answer be 2, or must it be 2cis(0)?

What if it's 2cis(pi)? Can I answer it as -2, or must it be 2cis(pi)?

It all depends on whether the question is asking for polar or cartesian form. Just writing -2 or 2 is cartesian form, whereas or are both in polar form.

Also,
should be written as as the restriction on the angle in polar form is .

[Special At Specialist]

I've never come across a question where they asked me to express a real number in polar form, but if that were the case then 2cis(0) would be correct.
Also note that you cannot say -2cis(0). You must say 2cis(pi), since the "r" value in rcis(θ) must always be positive.

[kensan]

I bought essentials 3rd edition off eBay last week, and the day after at school our teacher hands us the 2nd edition  -_-

[abd123]

If I am asked to give a complex number in polar form, and I get an answer like: 2cis(2pi), can the answer be 2, or must it be 2cis(0)?

What if it's 2cis(pi)? Can I answer it as -2, or must it be 2cis(pi)?

It all depends on whether the question is asking for polar or cartesian form. Just writing -2 or 2 is cartesian form, whereas or are both in polar form.

Also,
should be written as as the restriction on the angle in polar form is .

The arguement restricts between , a closed bracket shouldn't be there only an open bracket should exist.

[rife168]

If I am asked to give a complex number in polar form, and I get an answer like: 2cis(2pi), can the answer be 2, or must it be 2cis(0)?

What if it's 2cis(pi)? Can I answer it as -2, or must it be 2cis(pi)?

It all depends on whether the question is asking for polar or cartesian form. Just writing -2 or 2 is cartesian form, whereas or are both in polar form.

Also,
should be written as as the restriction on the angle in polar form is .

The arguement restricts between , a closed bracket shouldn't be there only an open bracket should exist.

That is correct, Thanks.
Fixed.