Suppose a vector \(\vec V\) makes an angle \(\phi\) with respect to the \(y\) axis.
is there a question here?
To find the components of the vector \(\vec V\) in the \(x\) and \(y\) directions, we can make use of the trigonometric functions.
Let's assume that the magnitude of \(\vec V\) is \(V\) units.
The component of \(\vec V\) in the \(x\) direction, denoted as \(V_x\), can be found by using the cosine function:
\[V_x = V \cdot \cos(\phi)\]
Similarly, the component of \(\vec V\) in the \(y\) direction, denoted as \(V_y\), can be found using the sine function:
\[V_y = V \cdot \sin(\phi)\]
The angle \(\phi\) can be either in radians or degrees, depending on the units you are using.
By substituting the value of the angle \(\phi\) and the magnitude \(V\), you can calculate the values of \(V_x\) and \(V_y\).