calculating vectors with component method. F1=1.96 N @ 60 degrees F2=1.96 N @ 120 degrees Fr=? @ ? degrees?

Adding vectors works best in Cartesian coordinates, which is probably what "component method" means.

F_r = 1.96 << cos 60, sin 60 >> + 1.96 << cos 120, sin 120 >>

= << 1.96(cos 60 + cos 120), 1.96(sin 60 + sin 120) >>

= 1.96 << 0, 2*sin 60 >> . . . . since cos 120 = cos (180-60) = - cos 60 and sin 120 = sin (180-60) = sin 60

= 1.96 << 0, √3 >>

~~ << 0, 3.39 >>

That/s 3.39 N at 90 degrees. Easy to see since the result is in the +y direction, right?

About the inverse tangent...yes, that's what they teach you; but I've generally found that the inverse cosine works better when the magnitude of the vector is (or will be already known). It never blows up and the sign choice of the result is determined by the sign of the y coordinate.

Forget numbers and lets convert the vector <<x,y>> (using double angle brackets for vectors, if that's not obvious) into "polar" <<r, θ>> form. Pythagoras get the value of r easily:

r = √(x² + y²)

Now you know that the reverse mapping gives you:

<<x, y>> = << r cos θ, r sin θ >>

So x = r cos θ which makes cos θ = x/r and θ = ± cos⁻¹ (x/r).

To choose the right sign, make that ± a minus sign if y<0 or plus if y is positive or zero. There are no blowups on vertical vectors, and the sign-fixup at the end is easy to remember.

I'll use this version whenever r is know, particularly when writing computer software, where handling and/or avoliding zero division blowups is annoying.

Not sure what the problem is but when I do cos and sin for F1 and F2 and when I have to add results X component adds to be 0 and I can't use that number in inverse tan calculation.

Please show work so I can understand better. Thank you in advance!