You are to program a robotic arm on an assembly line to move in the xy-plane. Its first displacement is A⃗ ; its second displacement is B⃗ , of magnitude 6.41cm and direction 62.7∘ measured in the sense from the +x-axis toward the -y-axis. The resultant C⃗ =A⃗ +B⃗ of the two displacements should also have a magnitude of 6.41cm , but a direction 22.3∘ measured in the sense from the +x-axis toward the +y-axis.
Find the component Ax of A⃗ .

Question

You are to program a robotic arm on an assembly line to move in the xy-plane. Its first displacement is A⃗ ; its second displacement is B⃗ , of magnitude 6.41cm and direction 62.7∘ measured in the sense from the +x-axis toward the -y-axis. The resultant C⃗ =A⃗ +B⃗  of the two displacements should also have a magnitude of 6.41cm , but a direction 22.3∘ measured in the sense from the +x-axis toward the +y-axis.
Find the component Ax of A⃗ .