how the hell do i solve for this??? where do i start??? dont i make them equal to eachother, or something?

Question

+F*cos(ϑ)-3000=0
+F*sin(ϑ)+1000=0

Answer 1

its simple,

F = 3000/cos x

F = -1000/sin x

equate the two equations:

F=F
3000/cos x = -1000/sin x

solve for x

tan x = -1000/3000
x = arctan -1/3
x = -18.43494882

just substitute the value of x to solve for F.

Answer 2

The trick is remembering that sin^2 ϑ + cos^2 ϑ = 1.

Change the first equation to Fcos ϑ = 3000 and square both sides. You get F^2cos^2 ϑ = 9000000. Do the same with the other one. Add the two equations together. I'm sure you can figure out the rest.

Answer 3

Fcos(x) = 3000
cos(x) = 3000/F

Fsin(x) = -1000
sin(x) = -1000/F

cos²(x) + sin²(x) = 9,000,000/F² + 1,000,000/F²
1 = 9,000,000/F² + 1,000,000/F²
F² = 10,000,000
F = ±1000√10

1000√10 cos x = 3000
cos x = 3/√10
x = 0.32175 radians

1000√10 sin x = -1000
sin x = -1/√10
x = -0.32175 radians

but
-1000√10 cos x = 3000
cos x = -3/√10
x = 2.1898 radians

if you check the graphs (or otherwise analyze possibilities), at x = -0.32175 both equations are true, and repeats at intervals of 2π.

Answer 4

Set the two equations equal and use the identity (Sinx)^2 + (Cosx)^2 = 1.