VCE Methods Question Thread!

[Zealous]

What timmeh is trying to explain to you is that ALL the familiar rules of calculus for circular functions only apply if the angles are in radians.

For instance, when we say that the derivative of sinx is cosx, this is only true if the angle x is in radians.
If the angle x is not in radians, it must be converted to radians. Converting the angle from degrees to radians involves the multiplication of x by a constant, which introduces the requirement to apply the chain rule when we differentiate.

If is working in radians, the derivative of is (the usual derivative formula only applies for radians), so if you're working in degrees, the derivative of is .

Ah I see. Thank you for clarifying!~

[darklight]

Is it possible to do this question? y= modulus of (cos(x)). The rate of change of y with respect to x at x=a, where pi/2 <a< 3pi/2 is...
Couldn't there be two solutions sin(a) and - sin (a) dependent on where a is between pi/2 and 3pi/2? Book says there is only one (sin (a))

[Alwin]

Is it possible to do this question? y= modulus of (cos(x)). The rate of change of y with respect to x at x=a, where pi/2 <a< 3pi/2 is...
Couldn't there be two solutions sin(a) and - sin (a) dependent on where a is between pi/2 and 3pi/2? Book says there is only one (sin (a))

Look at the domain of a.

[Eugenet17]

are we supposed to know how to solve a system of 3 equations with matrices by hand, or just with a calculator?

[Alwin]

are we supposed to know how to solve a system of 3 equations with matrices by hand, or just with a calculator?

expectation is CAS for any matrix bigger than a 2x2, so the qs are generally not worth many marks. if you're interested, pm me and I can link you / explain some methods by hand. however, these methods will be knowledge for the sale of knowledge

[b^3]

expectation is CAS for any matrix bigger than a 2x2, so the qs are generally not worth many marks. if you're interested, pm me and I can link you / explain some methods by hand. however, these methods will be knowledge for the sale of knowledge

There's also this which a couple of us put together a while ago:
1. Re: BORED already? Want to learn a bit of maths? :P
2. Re: BORED already? Want to learn a bit of maths? :P
So if you're interested then give it a look, otherwise don't worry about it. As said above, just make sure you know how to solve it on CAS and you'll be fine.

[Eugenet17]

okay cool, i'll check out the thread, thanks guys

[zhe0001]

Confused with this question, don't even know where to start

Combine a dilation of factor 2 from the x-axis and factor 3 from the y-axis to find the new coordinates of the square (0, 0), (1, 0), (1, 1), (0, 1).

P.S This is in the matrix chapter of my year 11 methods book - transformation of matrices

Any help is appreciated!

Thanks!

[Alwin]

Confused with this question, don't even know where to start

Combine a dilation of factor 2 from the x-axis and factor 3 from the y-axis to find the new coordinates of the square (0, 0), (1, 0), (1, 1), (0, 1).

P.S This is in the matrix chapter of my year 11 methods book - transformation of matrices

Any help is appreciated!

Thanks!

Using matrix method,


you can set up each point eg:


Then, multiply the two matrices to find the image eg:


ADDED: Now, there is also an intuitive method:
Dilation of factor 2 from x-axis --> means all the y-values are multiplied by 2:
(0, 0), (1, 0), (1, 1), (0, 1)  --> (0, 0), (1, 0), (1, 2), (0, 2).

Dilation of factor 3 from y-axis --> means all the x-values are multiplied by 3:
(0, 0), (1, 0), (1, 2), (0, 2) --> (0, 0), (3, 0), (3, 2), (0, 2).

Notice it is no longer a square

[shadows]

You need to create a transformation matrix

of dilation factor of 2 from x axis... and factor 3 from y axis....

times them together to get the transformation matrix  (2 by 2) and times it to the (co ordinates)  (2 by 1)

to get a (2 by 1) "image" of the coordinates.

I havent really touched matrix in ages so someone feel free to correct me if all im saying is wrong D:

[zhe0001]

Using matrix method,


you can set up each point eg:


Then, multiply the two matrices to find the image

Thank you! What does image mean?

[shadows]

The values that have been modified by the transformations

The Preimage would be the co-ordinates given before transformation is applied

[zhe0001]

The values that have been modified by the transformations

Preimage are would be the co-ordinates given before transformation is applied

oh ok thanks!

[zhe0001]

Not really sure how to get correct question, please help,

If,



then Find |A|

I understand that you find the dashes represent absolute value, and this was my answer,



but the answers say |A| is 6
How?

Please explain,

Thanks!

[Eugenet17]

|A| is determinant