Prove the ellipses:
where k is an arbitrary real number
have the same area as the ellipse
Last edited by Paradoxica; 20 Nov 2017 at 12:53 AM.
If I am a conic section, then my e = ∞
Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.
Letting the value of the solution to x = cos(x) be r, the following area expressions are obtained through integration:
A₁ = sin(r) - r²/2
A₂ = 1 - sin(r) + r²/2
A₂ - A₁ = 1 - 2sin(r) + r²
r > sin(r) (proof is trivial and left as an exercise)
- 2sin(r) > - 2r
1 - 2sin(r) + r² > 1 - 2r + r² = (1-r)² > 0
A₂ - A₁ > 0
A₂ > A₁
If I am a conic section, then my e = ∞
Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.
These pls
Capture.JPG
Capture 2.JPG
Could show me some working pls. Sorry for the trouble
Never mind, I got it. Cheers, the advice made things easier.
This one pls
Capture 3.JPG
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Appreciate some help with this: Find the range of values of |z| and arg(z) for |z-4-4i|=2sqrt(2)
Find an expression for cos^4x in terms of cos4x and cos2x
Edit: The question is from terry lee so I'm guessing it implies that you use 4U complex techniques rather than 3U, I'm not sure if you can even use 3U for this...
Therefore, using 3U method:
Last edited by Drongoski; 10 Jan 2018 at 8:34 PM.
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It is is circle of radius centred at 4+4i.
The construction is as follows
Join the points 4+4i (centre C) and origin O, extend this line so that it touches the circle again at B. This line OB will give us the range of values for |z|
To find the arg z, construct a diagram, observe the points E and F where the arg z is max and min, form a right angled triangle. The ratios of the sides will give the external angles, and from there using symmetry, the angles formed by the tangent at E and F at the origin, gives the max and min of the arg z.
In this problem |z| is from
and arg z is from
next question:
using demoivre's theorem or some other complex number theorems, find the exact value of cos 36 degrees.
go...
z= x+iy, w = u+iv; w = z -1/z. , find locus of w if |z|=2
edit:from patel textbook
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