Alan

There's a really good book by Paul Nahin called "An Imaginary Tale The Story of sqrt(-1)", published by the Princeton University Press, that is worth reading if you want to find out about the history and the uses of complex numbers.

Enter 2nd followed by asin.  (asin, or arcsine is sin^-1)

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Ignore my last comment!

On second thoughts, the minus sign should take this into account automatically!

1.  -1, 0, 1

2.  Infinite nbr. e.g -1/2, 1/2, 3/2

3. If we interpret integer as positive whole number, then 1

4. Infinite nbr: -sqrt(2), sqrt(2), sqrt(3)

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Oops! You'll need to think a little more carefully for the angle with the positive y axis.  The method above will give the angle with the negative y axis.

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Unit vector in x-direction ux = i 

A.ux = |A|*|ux|*cos(thetax)

(3i- 6j + 2k).(i) = 3        (because i.i = 1,  j.i = k.i = 0)

|A| = sqrt(3^2 + 6^2 + 2^2) → 7

|i| = 1

Hence:  3 = 7*1*cos(thetax)

cos(thetax) = 3/7

thetax  ≈ 64.6 degrees

Do a similar calculation for y and z, bearing in mind that the unit vector in the y direction is j, that in the z direction is k, and i.j = k.j = 0, j.j = 1, k.i = k.j = 0, k.k = 1

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83.333.... Million

Let x = 0.24242424.......

100x = 24.24242424......

Subtract the first from the second:

99x = 24

x= 24/99.    Or x = 8/33

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As far as I can see there is only one real number solution:

1). Underestimate. The curve is always positive, it decreases to the right but the decrease reduces.  Rectangles started from the right are therefore always under the curve.  Think of the function e^ -x for example.

2).  Overestimate. The straight line joining at the tops of the trapezoids are always use above the curve.

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