VCE Specialist 3/4 Question Thread!

[saba.ay]

How would I do the following?

cos^(-1)(tan(-pi/2))

(tan(-pi/2) gives undefined, but the answer is pi ? :/

[BubbleWrapMan]

It's undefined

[507]

Could someone please explain this part.

[Phy124]

Could someone please explain this part.

I made a post about this sort of thing a while back, it might help:

Re: Specialist Question Thread!

[507]

I made a post about this sort of thing a while back, it might help:

Re: Specialist Question Thread!

Perfect, thanks

Would we be able to use that in the exam, or would we be expected to do something like let and solve provided and

[lzxnl]

The problem with introducing a square root is that you then introduce extra solutions. You'll have to check every solution you find at the end. Also, introducing a square root can make equations messier than they need to be.

[Holmes]

I'm having trouble applying the double angle formula to find tan(pi/12), could someone please demonstrate? :)Thanks for helping!

[Hancock]

Let



Let





http://www.wolframalpha.com/input/?i=tan(pi%2F12)

Solving this quadratic and taking the positive root (since tan(pi/12) > 0 since it's in the first quadrant).

[Henreezy]

We just began Calculus in spesh and I'm unsure how to differentiate this using the chain rule

dy/dx=tan^4(2x)

EDIT:

I approached the question by doing this:
using dy/du = 4[]^3 and du/dx = 2 sec^2(2x)
4[tan(2x)]^3 x 2sec^2(2x) giving me the answer of 8 sec^2(2x) tan^3(2x)

I'm not sure that's right also, does the 8 apply to both the tan and the sec?

[Phy124]

We just began Calculus in spesh and I'm unsure how to differentiate this using the chain rule

dy/dx=tan^4(2x)

Note that

Let and or whichever method you prefer.

[Stick]

I seem to be stuffing up every single differentiation of an an inverse circular function when there's a co-efficient in front. I'd really appreciate it to see the worked solution of the following question. It might help me determine where I'm going wrong. Thanks.

[Professor Polonsky]

So basically, will I need to know this?

[Phy124]

I seem to be stuffing up every single differentiation of an an inverse circular function when there's a co-efficient in front. I'd really appreciate it to see the worked solution of the following question. It might help me determine where I'm going wrong. Thanks.

(Image removed from quote.)

Coefficients eh?

Remember that and you shouldn't have to many problems with them i.e. take it out the front at the start and draw some massive brackets around the rest of the expression

For the question at hand;

Let and

[Limista]

Question 1:
How can I solve

x⁴ - 9x³ - 175x² - 267x + 31050 = 0

algebraically WITHOUT using calculator?

Question 2: Set up simultaneous equations that could be used to find (-142 + 65i)^(1/3) in exact Cartesian form. Do not attempt to solve these equations.

Thanks

[Daenerys Targaryen]

Factorise it; by letting x=random numbers, and hope that it =0. Which means its a factor.