VCE Specialist 3/4 Question Thread!

[VanillaRice]

RTP: cosec(x) + cot(x) = cot(x/2) where sin(x) =/= 0.

So far all I have done is:

Spoiler

But now I don't even know if that's of any use...

Any thoughts?

The fact that there is both x, and x/2 immediately tells me that some form of double angle formula is involved. See where that takes you

[Immune_Sushi]

Hello ,
Does anyone have a procedure for solving inequations such as this:


and can the same procedure apply for:

[VanillaRice]

Hello ,
Does anyone have a procedure for solving inequations such as this:


and can the same procedure apply for:

I find that the best way is to draw a graph. You can either draw y = |5-x| and y = |4x+2| individually, or transpose to make the equation |5-x| - |4x+2| < 0, draw the left hand side as a graph (y = |5-x| - |4x+2|), and see where it is less than zero.

Hope this helps

[Sine]

Hello ,
Does anyone have a procedure for solving inequations such as this:


and can the same procedure apply for:

perfect graphing since it's a region you can use a testpoint to confirm the area

EDIT: VanillaRice by 13 seconds

[Immune_Sushi]

Thanks Sine and VanillaRice!
Is VCAA allowed to ask this kind of question though?

[Sine]

Thanks Sine and VanillaRice!
Is VCAA allowed to ask this kind of question though?

I would be suprised if it came up tbh since VCAA  have a lot more important topics to be put on the exam.

[noregret]

Hello, how do solve find the volume of solid of revolution rotated about the x axis or the y axis.

For example, how do I solve area bounded by y=x^2,  y=-x(x-2）

Area bounded by y=x^1/2, y=4 and the y-axis

Area bounded by x=y^2, y=-1, y=1 and the y axis.

[keltingmeith]

Hello, how do solve find the volume of solid of revolution rotated about the x axis or the y axis.

For example, how do I solve area bounded by y=x^2,  y=-x(x-2）

Area bounded by y=x^1/2, y=4 and the y-axis

Area bounded by x=y^2, y=-1, y=1 and the y axis.

Which axes are each being rotated about? As that will change the answer.

[noregret]

Which axes are each being rotated about? As that will change the answer.

Thanks for your reply, for the first question, it rotates around the x axis and for second and third questions they both rotate around the y axis.

[Shadowxo]

Hello, how do solve find the volume of solid of revolution rotated about the x axis or the y axis.

For example, how do I solve area bounded by y=x^2,  y=-x(x-2）

Area bounded by y=x^1/2, y=4 and the y-axis

Area bounded by x=y^2, y=-1, y=1 and the y axis.

The volume when rotated around the y axis is

and when rotated around the x axis is


So if the graph of y=x^1/2 between y=4 and the y axis is rotated around the y axis, we know the boundaries are y=4 (given), and y=0 as the y axis is where x=0, so y=0^1/2=0

From there it's just standard integrals. The other questions should follow a similar format.

If you want to find the volume where the area between two graphs is rotated, you subtract one volume from the other. That is:
The volume when rotated around the y axis is

Note f(y) is just like the x from before, basically x in terms of y.

and when rotated around the x axis is


Note: drawing it out is very useful

[Yertle the Turtle]

How far behind am I if I haven't yet started the year for Spesh, because my distance school hasn't yet let me connect? Is there anything I should particularly start on straight away?

EDIT: Post #500!!! 

[VanillaRice]

How far behind am I if I haven't yet started the year for Spesh, because my distance school hasn't yet let me connect? Is there anything I should particularly start on straight away?

EDIT: Post #500!!! 

Many classes have already had a holiday head-start (with possible classes before the year ended last year). That being said, you are not too disadvantaged, but I would recommend starting as soon as possible (given the school term has already started). Do you have access to your textbook? Trigonometry (including reciprocal and inverse trig functions) is a topic that is usually covered early on. You could also consider smaller topics, like reciprocal functions, quotient functions or absolute value. All these topics are included in Area of Study 1.

Good luck

[microwaverdetective]

If A and B are acute angles such that sin(A) = 3/5 and cos(B) = 5/13, find tan(A+B) without evaluating A or B.
Working please! Cheers

[Shadowxo]

If A and B are acute angles such that sin(A) = 3/5 and cos(B) = 5/13, find tan(A+B) without evaluating A or B.
Working please! Cheers

For this you have to use the addition formulae. You could use the tan one but that would result in more tans and hence be more annoying to work out.

From there you just need to find sin(B) and cos(A), which you can find using sin²(x)+cos²(x)=1, and if they're acute angles (quadrant 1) they must both be positive.
Let me know if you need any more help!

[noregret]

Hello, how do I find the sum of all multiples of 6 between 100 and 600
Sum=102+108+114+.....+594
If Un=a+(n-1)d I know the Un=594 and a=102, but I cannot get n and d.