# Further Maths Argand Diagrams

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#1
Any ideas on 4b? Thank you!
0
2 years ago
#2
Part a) must be a circle, radius 5, centered on (6,1).
Part b) Translates the origin to (11,10), then you have to find the smallest angle (most minimum) of a point on the circle from the new origin.
Can you sketch it?
0
2 years ago
#3
(Original post by IzzyLJB)
Any ideas on 4b? Thank you!
is a half-line starting from going off in some direction (blue line in my diagrams below)

The direction is limited though, because must be on the circle that is defined by (you sketch this circle in part a, it is the red one in my diagram).

Hence you are seeking for the minimum argument of the blue half-line (angle measured from the black dotted line in my diagram, labeled ) such that there is some intersection with the circle.

You need to look at two extremes. One of which is the following:

Spoiler:
Show

or this one:

Spoiler:
Show

Which one do you think represents the MINIMUM argument?? Work with that diagram and derive the answer for .
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4 weeks ago
#4
Can anyone help me with part b ? I'm guessing the minimum arguement is pi/2 right? So where do I go from here?
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4 weeks ago
#5
I think I've got it please correct me if I'm wrong, or if I need to be more elaborate. See the attactched file.
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4 weeks ago
#6
Looks good.
0
4 weeks ago
#7
(Original post by mqb2766)
Looks good.
Is it worthy of full marks?
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4 weeks ago
#8
Pardon me, I forgot to put that sqrt(9^2 + 5^2)=sqrt(106)
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4 weeks ago
#9
Is it worthy of full marks?
It's a bit messy, but has the main points in. Hard for me to judge if you may be docked a mark.
For instance, you could describe why the two triangles are congruent, why the min angle corresponds to the tangent ... if you want to be guaranteed full marks. However, I don't have the mark scheme.
Last edited by mqb2766; 4 weeks ago
0
4 weeks ago
#10
(Original post by mqb2766)
It's a bit messy, but has the main points in. Hard for me to judge of you may be docked a mark.
For instance, you could describe why the two triangles are congruent, why the min angle corresponds to the tangent ... if you want to be guaranteed full marks. However, I don't have the mark scheme.
I'm guessing we'd have to ask the OP IzzyLJB can you give the source of this question to me?
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4 weeks ago
#11
It is 2 years old and the OP hasn't logged on for several months. You've got the right method, so Id just move on?
0
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