Area of a Region: A maths
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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!
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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?
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Originally posted by skythewood:
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. -
Originally posted by skythewood:
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. -
Originally posted by bonkysleuth:
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.
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Originally posted by skythewood:
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. -
Originally posted by bonkysleuth:
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.
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Yea but I still don't know why 5/6 pi should be rejected.
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Originally posted by bonkysleuth:
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?
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Originally posted by skythewood:
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) -
Originally posted by bonkysleuth:
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)ok. go and learn now and draw it.
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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
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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 -
Originally posted by bonkysleuth:
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!
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...
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Originally posted by wee_ws:
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 Shiheh 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.
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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 -
Originally posted by wee_ws:
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 ShihYup thanks. What you don't use, you lose. Haven't been doing function transformation for a long time. :)