Area of a Region: A maths

bonkysleuth SG

The diagram shows part of the curve y = sin(2x + pi/3)

Find the x-coordinate of the point A where the curve cuts the x-axis. For positive value answers, I obtained pi/3 and 5pi/6... However the actual answer is pi/3. I see no reason why we should reject 5pi/6. Would someone please explain to me? Thank you!

skythewood SG

draw the sine graph out, from x = 0 to x = pi. Than you will see the sine graph intercept the x-axis twice.

one of them is point A. understand?

bonkysleuth SG

draw the sine graph out, from x = 0 to x = pi. Than you will see the sine graph intercept the x-axis twice.

one of them is point A. understand?

But why do you draw from x = 0 to x= pi? It doesn't make much sense to me.

bonkysleuth SG

draw the sine graph out, from x = 0 to x = pi. Than you will see the sine graph intercept the x-axis twice.

one of them is point A. understand?

But why do you draw from x = 0 to x= pi? It doesn't make much sense to me.

skythewood SG

But why do you draw from x = 0 to x= pi? It doesn't make much sense to me.

sketch... your graph..... from x=0.... to x= pi.

Do it.

bonkysleuth SG

sketch... your graph..... from x=0.... to x= pi.

Do it.

the points that cut the x-axis of sine graph are 0, 0.5pi and pi.

skythewood SG

the points that cut the x-axis of sine graph are 0, 0.5pi and pi.

similarly, for y = sin(2x + pi/3), the graph cuts the x -axis at which 3 points?

from this you can understand le. Good job.

bonkysleuth SG

Yea but I still don't know why 5/6 pi should be rejected.

skythewood SG

Yea but I still don't know why 5/6 pi should be rejected.

seriously, sketch out the graph,y = sin(2x + pi/3), from x=0 to x = pi, label the 2 intercepting points accordingly.

compare your sketch to the given diagram. Which one looks more like point A to you?

bonkysleuth SG

seriously, sketch out the graph,y = sin(2x + pi/3), from x=0 to x = pi, label the 2 intercepting points accordingly.

compare your sketch to the given diagram. Which one looks more like point A to you?

I just checked. We weren't taught to draw graphs like sin(2x + pi/3). We only learnt graph drawing for equations like 4sin3x + 1 where there is only 1 term with the trigo equation and not joined together like sin (2x +pi/3)

skythewood SG

ok. go and learn now and draw it.

eagle SG

Hi Bonkysleuth, it would help you a lot if you could plot/draw out the graph, as pointed out rightly by skythewood.

You can try using the software winplot

wee_ws SG

Hi,

Sketching y = sin (2x + pi/3) is not difficult.

Carry out these steps in sequence:

1. Sketch y = sin x.

2. Shift the graph pi/3 units to the left.

3. Now, carry out a stretch of the graph by a scale factor of 1/2. You should know what a stretch is, given that you have been taught how to sketch y = 4 sin 3x + 1.

Graph sketching is a really important skill that ought to be mastered well.

Thanks!

Cheers,
Wen Shih

Mikethm SG

The diagram shows part of the curve y = sin(2x + pi/3)

The explanation is very simple... the curve does cut the x-axis at pi/3 and 5pi/3 yes... BUT LOOK AT YOUR DIAGRAM!!! YOU WANT THE 1ST POINT WHERE THE CURVE CUT THE X-AXIS... Which come 1st? pi/3 or 5pi/3???

Isn't the answer obvious?

Sorry for the caps but that is the way I ram in simple logic...

Mikethm SG

Hi,

Sketching y = sin (2x + pi/3) is not difficult.

Carry out these steps in sequence:

1. Sketch y = sin x.

2. Shift the graph pi/3 units to the left.

3. Now, carry out a stretch of the graph by a scale factor of 1/2. You should know what a stretch is, given that you have been taught how to sketch y = 4 sin 3x + 1.

Graph sketching is a really important skill that ought to be mastered well.

Thanks!

Cheers,
Wen Shih

eh I think you got careless or I too long never do functions liao.

It should be?

1. Sketch y = sin x

2. Convert it to y = sin(2x) by dividing the x-values by 2. (aka stretch by 1/2)

3. Convert to y = sin (2x+pi/3) by shifting it pi/3 units to the left.

Correct me if I am wrong coz very long never do this technique is now taught at A level instead of O level.

wee_ws SG

Hi Mikethm,

If scaling comes first, translation will then be pi/6 to the left in your step 3.

If translation of pi/3 comes before scaling (as in my description), the resulting scaling will still become pi/6 to the left.

For more details about the ordering of transformations (which is often confusing), please read my article at:

http://www.freewebs.com/weews/graphtransformations.htm

Thanks again :)

Cheers,
Wen Shih

Mikethm SG

Hi Mikethm,

If scaling comes first, translation will then be pi/6 to the left in your step 3.

If translation of pi/3 comes before scaling (as in my description), the resulting scaling will still become pi/6 to the left.

For more details about the ordering of transformations (which is often confusing), please read my article at:

http://www.freewebs.com/weews/graphtransformations.htm

Thanks again :)

Cheers,
Wen Shih

Yup thanks. What you don't use, you lose. Haven't been doing function transformation for a long time. :)