VCE Specialist 3/4 Question Thread!

[Daenerys Targaryen]

there shouldn't even be a line connecting the origin to the point. also, in the exam they usually give an argand diagram with dotted circles on it anyway. any point on its path must have coordinates
hence, where
and where
since , where

But does that mean if you subbed that ellipse equation back into r(t)=_______=1? Can you do that? Or once you change it to parametric equations it changes everything?

[polar]

But does that mean if you subbed that ellipse equation back into r(t)=_______=1? Can you do that? Or once you change it to parametric equations it changes everything?

but r(t) is a vector and 1 isn't so r(t) can't be equal to 1.

if you substitute in a value of  into r(t) you'll get a vector, lets say it's ai+bj, then if you do that will always equal to 1. basically, any coordinate along the path of the red light satisfies that condition while r(t) itself doesn't equal to 1.

[Holmes]

Find the domain and range for where the composite function sin(arccos x) exists.

The range of the inner function has to a subset of the domain of the outer function.
The range of the inner function arccos x is equal to [0,pi]
The domain of the outer function sinx is equal to [-pi/2, pi/2]
We must restrict it, so that the range of arccos x becomes [0, pi/2]

I'm confused from here onwards. How is it done? Please explain the concept behind it, i've got worked solutions but they don't make sense to me. Thanks!

[abcdqd]

Find the domain and range for where the composite function sin(arccos x) exists.

The range of the inner function has to a subset of the domain of the outer function.
The range of the inner function arccos x is equal to [0,pi]
The domain of the outer function sinx is equal to [-pi/2, pi/2]
We must restrict it, so that the range of arccos x becomes [0, pi/2]

I'm confused from here onwards. How is it done? Please explain the concept behind it, i've got worked solutions but they don't make sense to me. Thanks!

use your restricted arcos x range to find the restricted domain of arcos x. from the graph, we can see that this is [0,1] => this becomes the domain for the composite function.
now to find the range of the composite function, you use the restricted range of arcos x, as these are the only values you can take the sin() of. so the range of sin() over [0,pi/2] is [0,1] => this is the range of the composite function

[bonappler]

Question d, thanks

[Conic]

Find the 2 factors:





Let the polynomial equal P(z):





You can use the same method for the second part.

[Will T]

Just need some help with Essentials Chapter 3D
Questions: 9, 10, 11 and 19.

[Conic]

19:
Let the length of the straight portion of the string = x

(Circle mensuration from GMA)





Since







q.e.d.

[b^3]

EDIT: .......where'd the question go?

As we have the differential equation in terms of , we need to flip everything so that we can integrate with respect to . Then don't forget to add the constant of integration and them use the initial condition, that the mass is at time .

Spoiler

That is it takes years to decay to half the initial mass.

[Homer]

hey thanks b^3, i worked out the answer a minute after i posted, and deleted my post :-/  but thanks anyways

[barydos]

Anyway, what exactly does part e) mean when it says A=E?

Edit: Also.. actually I'm not quite sure how to do part f) ii)

[Stick]

I was doing this very question just last night, so you're in luck! Don't worry, I found it tricky too and I had to refer to my solutions supplement at times to figure it out.

For part e: By A=E they mean that they are the same point, thus creating a square inside the circle. Thus, the sum of the internal angles must be 360 degrees. See if you can go from there.

For part f ii: Let x=cos(pi/5) and substitute the given value into the equation. By showing it equals zero, you are proving that it is in fact the correct value.

[thecreeker]

Prove that cosec(x)+cot(x)=cot(x/2)
keep getting stuck at a certain point, help would be appreciated?

[barydos]

I was doing this very question just last night, so you're in luck! Don't worry, I found it tricky too and I had to refer to my solutions supplement at times to figure it out.

For part e: By A=E they mean that they are the same point, thus creating a square inside the circle. Thus, the sum of the internal angles must be 360 degrees. See if you can go from there.

For part f ii: Let x=cos(pi/5) and substitute the given value into the equation. By showing it equals zero, you are proving that it is in fact the correct value.

e) Does it become a square because it must adhere to the AB = BC  =.... property?
otherwise wow so the BOA = 90deg so theta = 45 or pi/4 ??!!!

f) ii)  sorry Stick, I'm still not sure what to do :S
having got
after subbing , I'm kinda stumped :S

[polar]

Prove that cosec(x)+cot(x)=cot(x/2)
keep getting stuck at a certain point, help would be appreciated?

Let then,