Thread: solving help required

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

to add to that, by dividing the equation and by substitution method, we can find the value, but i dont know how to solve the equations.

Originally Posted by sanmo4

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

thanks for your reply... thanks for your explanation. the answer am getting by substitution also same..