(09-15-2011, 11:29 PM)PartyPaint Wrote:

(08-28-2011, 06:16 PM)Frooxius Wrote: Shining White Holmse: Pfff, that's simple Though you forgot to specify if the values are degrees or radians, but judging from the values, they're degrees.

The result is:
sqrt(0.5) which is approximately 0,70710678118654752440084436210485

That's because it's the cos(90°)/tan(45°) results in zero, because cos(90°) is zero, so only sin(45°) is needed to calculate.

If you use a right triangle with hypotenuse length equal to 1 and with angle 45°, then two remaining sides are equal. Therefore:
c = 1
a = b = ?
Sides a and b represent sin(45°) and cos(45°) so
a = b = sin(45°) = cos(45°) = d

And from the Pythagorean we know that
c^2 = a^2 + b^2
Which is
1^2 = sin(45°)^2 + cos(45°)^2
But we know that they're equal so we can do this:
1 = d^2 + d^2
Which is
1 = 2(d^2)
And we need to know d, which equals both to sin(45°) and cos(45°), so we extract it:
1/2 = d^2
sqrt(1/2) = d
So we get
d = sqrt(0.5)
And we substituted sin(45°) with d so the final result is:
sin(45°) = sqrt(0.5)