With the x axis in the direction of A, the sum of the x components = A + Bcosq and the sum of the y components = -Bsinq . So the resultant is

R = [(A + Bcosq )² + (Bsinq )²]^1/2
at angle ATN[(-Bsinq )/(A+Bcosq )]

Note: A calculator will tell you that the angle is negative. The direction of R is always between the two, and in this case below the x axis. If we had chosen the x direction to be along B, we would have a positive angle.

If the total x were negative and y positive, the calculator would give you the same result, but this would be off by 180^o. The rule is: If the sum of x components is negative, add 180^o to your calculator's answer.

Now go back to vectors or to the beginning physics page.

My other main pages:

fluids, heat, electricity and magnetism
vibrations and waves
quantum

Comments, questions: email fredrick.gram @tri-c.edu (remove space before @)