Question

Vector A has a magnitude of 16.5 units and it points in a direction 340 counterclockwise from the positive x-axis. What are the x- and y- components of A?

Answer 1

We can find the components as:

$\begin{gathered} A_x_{}=16.5\cos (340) \\ A_x=15.5 \\ ------------ \\ A_y=16.5\sin (340) \\ A_y=-5.64 \end{gathered}$

$\begin{gathered} \sin (C)=\frac{opposite}{_{\text{ }}hypotenuse}=\frac{Ay}{A} \\ so\colon \\ _{\text{ }}if_{\text{ }}we_{\text{ }}solve_{\text{ }}for_{\text{ }}Ay \\ Ay=A\sin (C) \end{gathered}$$\begin{gathered} \cos (C)=\frac{adjacent}{_{\text{ }}hypotenuse}=\frac{Ax}{A} \\ so\colon \\ _{\text{ }}if_{\text{ }}we_{\text{ }}solve_{\text{ }}for_{\text{ }}Ax \\ Ax=A\cos (C) \end{gathered}$