hi.
please help me to solve these equations
A*sin(atan(2000/B)*2) = 500
A*sin(atan(4000/B)*2) = 752.545
and explain it.
thanks
mohanraj
Umm, big numbers.
You know that arctan(U) is an angle.
It is an angle whose tan value is U.
So, in its reference triangle,
opposite side = U
adjacent side = 1
hypotenuse = sqrt(1 +U^2)
And then, sin(arctan(U)) = opp/hyp = U /sqrt(1 +U^2)
And, cos(arctan(U)) = adj/hyp = 1 /sqrt(1 +U^2)
To avoid plunging into very large numbers at once, let
arctan(2000/B) = angle X
arctan(4000/B) = angle Y
Thus, the original equations can be re-written as:
A*sin(2X) = 500 ---------(1a)
A*sin(2Y) = 752.545 ------(2a)
Spread those:
A[2sinXcosX] = 500 ---------(1b)
A[2sinYcosY] = 752.545 -----(2b)
To eliminate A, divide (1b) by (2b)
sinXcosX /sinYcosY = 0.664412 -------------(3)
Use the method in the sample U above and you'd get
sinX = 2000 /sqrt(B^2 +4,000,000)
cosX = B /sqrt(B^2 +4,000,000)
sinY = 4000 /sqrt(B^2 +16,000,000)
cosY = B /sqrt(B^2 +16,000,000)
Substitute those into Eq.(3)
Etc....
You should get B = 5700
And A = 800