VCE Methods Question Thread!

[soNasty]

how do i solve:

for by hand?

also, is the same as ??

[keltingmeith]

how do i solve:

for by hand?

also, is the same as ??

Null factor. Either -3sin(2x)=0 or cos^2(2x)=0. Solve as normal.

As long as the angles are the same, then sin^2(x)+cos^2(x)=1. So, this means that sin^2(2x)+cos^2(2x)=1 as well, as the angles are the same.

[kinslayer]

Hi,

Could some help with the following question:

What is the value of ?

The question does not allow the use of a calculator and I would greatly appreciate if you could please explain it using the symmetry of the unit circle method.

Thanks

First draw a unit circle with the x- and y-axes.

Next, draw the -5pi/6 angle. It's pi/6 radians anticlockwise from the negative x-axis.

tan(-5pi/6) = sin(-5pi/6) / cos(-5pi/6).

There are a few ways you can do this, but the quickest is to note that the cosine of that angle (-5pi/6) will be the negative value of of the cosine of pi/6 (because the cosine is just the x-coordinate on the unit circle) and sin(-5pi/6) is just -sin(pi/6) (because the sine is just the y-coordinate on the unit circle).

Then tan(-5pi/6) = -sin(pi/6) / -(cos(pi/6)) = tan(pi/6) = 1/sqrt(3).

[M-D]

Thanks kinslayer for your answer.

This is how I did. Can you please correct this:

is in the 3rd quadrant. The symmetry rule for tan in the 3rd quadrant is:




Thanks 

[keltingmeith]

Thanks kinslayer for your answer.

This is how I did. Can you please correct this:

is in the 3rd quadrant. The symmetry rule for tan in the 3rd quadrant is:




Thanks 

They're the same answer - you've done nothing wrong.

[myanacondadont]

Hey I have a quick question. It says to express:



in the form of

 , where A,B and C are integers.

My intial reaction is to expand the secondary simplified form and then just equate them. In the answers they do that as well, however they already know that A = -1 before they expand it.

How do they know that?

[keltingmeith]

For any polynomial that can be placed in turning point form, the A you've given will be exactly the same as the coefficient of the variable with the highest degree.

[myanacondadont]

For any polynomial that can be placed in turning point form, the A you've given will be exactly the same as the coefficient of the variable with the highest degree.

Thank you very much!

[knightrider]

For this question relating to image attached

How far is it from the starting point when t = 7?

When you sub this into the displacement function would you have to also minus 6 from the answer as the skier starts 6m to the right of the origin

[M_BONG]

Strictly decreasing/increasing = inclusive right?

I always remember my teacher saying strictly increasing = meaning inclusive even if it's at a TP but this NEAP exam says otherwise? (re: attachments)


Also, are functions increasing/decreasing at inclusive endpoints?

Say, a question with function y= 2sin (t) +3  modelling the rate of traffic flow in an intersection, t E [0, 2pi]

A question then might ask over what interval is traffic flow increasing.

Is the traffic flow still increasing at t=  2pi? or do I put round brackets at 2pi?

Thanks

[psyxwar]

Strictly decreasing/increasing = inclusive right?

I always remember my teacher saying strictly increasing = meaning inclusive even if it's at a TP but this NEAP exam says otherwise? (re: attachments)


Also, are functions increasing/decreasing at inclusive endpoints?

Say, a question with function y= 2sin (t) +3  modelling the rate of traffic flow in an intersection, t E [0, 2pi]

A question then might ask over what interval is traffic flow increasing.

Is the traffic flow still increasing at t=  2pi? or do I put round brackets at 2pi?

Thanks

Yeah I'm pretty sure it's inclusive as well. A function is strictly increasing over an interval if f(b)>f(a), provided that b>a, for all a and b (given that a and b are elements of the interval).

[LiquidPaperz]

is that shaded part a trapezium? what makes something a trapezium, (e.g. the sides of the picture with blue base)

[psyxwar]

is that shaded part a trapezium? what makes something a trapezium, (e.g. the sides of the picture with blue base)

A trapezium (or trapezoid) is a quadrilateral (4 sides) with one pair of parallel sides. That's it, and the formula Area=  h/2*(a+b) holds true, where h is the height, and a and b are two of the side lengths.

Note that this means parallelograms are technically trapezoids (as they are defined as a quadrilateral with 2 pairs of parallel sides), and thus so are rectangles, squares, rhombuses. You'll notice the area formula holds true no matter what, even for these 'special cases'. For a rectangle, (a+b)/2 is just equal to the length, and height is the other side.

[LiquidPaperz]

A trapezium (or trapezoid) is a quadrilateral (4 sides) with one pair of parallel sides. That's it, and the formula Area=  h/2*(a+b) holds true, where h is the height, and a and b are two of the side lengths.

Note that this means parallelograms are technically trapezoids (as they are defined as a quadrilateral with 2 pairs of parallel sides), and thus so are rectangles, squares, rhombuses. You'll notice the area formula holds true no matter what, even for these 'special cases'. For a rectangle, (a+b)/2 is just equal to the length, and height is the other side.

Hey man, thanks. but could you pleasee dumben that down a a little haha.

i treated the shaded part as a trapezium, all calculations are right and hence used the formula and times it by 5 cause there were 5 of them and that got me the wrong answer...see

AT = 2.55m
AD = 0.55m

[psyxwar]

Guessing this is further, which I don't do so not sure if my answer is right. I'm not the greatest at geometry. You're better off posting to the further thread.

What was your working?

I've used area of a triangle = 1/2(b)(c)sin(theta) but i'm not sure if you're allowed to use that either.

Area of bench = Outer pentagon - Inner pentagon = 5(1/2(TA)(TB)sin(72)-1/2(TD)(TC)sin(72))

TA=TB=2.55

TD=TC=AT-AD=2.00

Therefore Area=5.95 units^2