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Mathematics: Post your doubts here!

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Hi guys,i got a problem here.Need help.A question no 10(b part 2).Thanks a lot.....
 

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Thanks a lot
umm.. what about part ii?
9709_s08_qp_3.pdf can someone solve Q5 please
Sorry I was feeling bored to solve part ii that time haha.
OK now,
substituting value of z and simplifying you get. 1 /(2cosθ+2)-2sinθ i
Multiplying by it's conjugate i.e. (2cosθ +2)+2sinθ i and again simplifying we get,
(2cosθ +2+2sinθ i) / 4cos^2θ + 8cosθ + 4 + 4sin^2θ
=numerator/ 8+8cosθ [4cos^2θ + 4sin^2θ = 4]
Now separating the real part only from numerator 2(cosθ +1) / 8(cosθ +1)
Hence real part = 1/4
 
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Hi guys,i got a problem here.Need help.A question no 10(b part 2).Thanks a lot.....
Can you give me the values of p,q,alpha and beta?
EDIT: OK I have solved it and I am going to attach the files hope you understand.
 

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Yes please someone explain this question with explanations for every step. I know how to do the diagram, im just having trouble finding the least value for z-w.
can you show me the diagram? I think we should find least value of |Z|-|W|
 
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I'd appreciate it ..
a)
f(x) = 4 - 3 sin x = 2
-3 sin x = -2
sin x = 2/3
x ≈ 0.7297276562... ≈ 0.73

b)
1 ≤ sin x ≤ 1
-3 ≤ 3 sin x ≤ 3
3 ≥ -3 sin x ≥ -3
7 ≥ 4 - 3 sin x ≥ 1

If k < 1 or k > 7, there is no solution.

c)
A = 3π/2

d)
g(x) = 4 - 3 sin x = y
4 - 3 sin y = x
4 - x = 3 sin y
(4 - x)/3 = sin y
sin^-1 (4 - x)/3 = y= g^-1

e)
g^-1 (3) = sin^-1 (4 - 3)/4 = sin^-1 1/4 = 2.8017557... ≈ 2.802

:)
 
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