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For questions like area under the graph or volume of revolution, do we need to re-draw the diagram given on the question paper onto our answer script?
Thank You!
Thank You!
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Mathematics: Post your doubts here!
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Nope. We do not have to draw anything until specified in question paper.For questions like area under the graph or volume of revolution, do we need to re-draw the diagram given on the question paper onto our answer script?
Thank You!
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Thank You!
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solving left hand side,
open up the bracket which gives u... cos^2x+6sinxcosx+9sin^2x
use the identity sin2x=2sinxcosx
so u need to get 6sinxcosx so multilpy it by 3... 3sin2x=6cosxsinx
equation becomes cos^2x+3sin2x+9sin^2x
so simplifying it further cos^2x+3sin2x+9(1-cos^2x)
cos^2x+3sin2x+9-9cos^2x
-8cos^2x+9+3sin2x
if u look at 5-4cos2x....its basically the same as -8cos^2x+9 when u simplify it so replace it with that...
thus 5-4cos2x+3sin2x proven
u need to show them how u converted the 5-4cos2x into -8cos^2x+9
open up the bracket which gives u... cos^2x+6sinxcosx+9sin^2x
use the identity sin2x=2sinxcosx
so u need to get 6sinxcosx so multilpy it by 3... 3sin2x=6cosxsinx
equation becomes cos^2x+3sin2x+9sin^2x
so simplifying it further cos^2x+3sin2x+9(1-cos^2x)
cos^2x+3sin2x+9-9cos^2x
-8cos^2x+9+3sin2x
if u look at 5-4cos2x....its basically the same as -8cos^2x+9 when u simplify it so replace it with that...
thus 5-4cos2x+3sin2x proven
u need to show them how u converted the 5-4cos2x into -8cos^2x+9
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Can someone please sketch the diagram for (b)(i) please?
So I know the first one is a circle with centre 2+i and radius 1
Now the second equation i solved
(x+iy+i)<(x+iy-2)
this gives
y>2x-1.5
So i drew a line like so...
Is it correct as the ms says this :
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Part ii please
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How do you find the least value of |z-w| ?
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Least value is the distance D-C
so find AC by using sine rule
AC = 3root2/2
DC = AC - 1
Since the radius of circle is 1
So DC = (3root2/2)-1 = 1.12
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Can you please show it in a diagram ?
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Red is y=x
Blue is y=(1/root3)x +2
I mean the argand diagram if you can please ?
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That is the same as the argand diagram ... y corresponds to imaginary axis and x corresponds to real axis
Can you please show how to obtain the answers using trigonometry on the diagram ?
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Magnifying the triangle we can find the angles and use the sine rule
The argument of blue line is given in question as pi/6
red is y=x hence the argument is pi/4
Knowing these 2 angles you can find the other angles
We know the blue line cuts the imaginary axis at 2 (when we solved the equation above) so the length will be 2
Now apply the sine rule as x = [2/sin(pi/2)] * [sin(2pi/3)]