For example, let us consider our old friend \(\vec{A} = 5 \hat\imath\ + 7 \hat\jmath\). Clearly, \(A_x = 5, A_y = 7\). The magnitude is thus, \(\sqrt{5^2 + 7^2} = 8.6\). The angle is \(\tan^{-1}\left(\frac{A_y}{A_x}\right) = \tan^{-1}\left(\frac{7}{5}\right) = 54^{\circ}\)