Consider a particle with initial velocity v⃗ that has magnitude 12.0 m/s and is directed 60.0 degrees above the negative x axis. What is the

60 degrees above the negative x axis means that we are in quadrant 2 so our x component will be negative.  TO find the x component we use the cosine function as it represents x values.  Our calculation looks like

V_x=12cos60=6

$$\begin{array}{rll}
cos60^0&=&\frac{\dot{x}}{12}\\\\
\dot{x}&=&12\times \frac{-1}{2}\\\\
&=&\:-6m/s
\end{array}$$

It can  be seen from the diagram that the velocity in the x direction must be negative.