Look at the force in space in this example.
The angle between the force and the y-axis
is given, and it is denoted theta sub y.
Using this information, we can easily find
the y-component of the force using the angle
theta.
It is equal to the magnitude of the force
times the cosine angle.
The y component of this force is shown using
the dotted line on the y-axis in this diagram.
However, we don’t know the other two angles
between the force and the axes, x and z, but
we do know one more angle, which is on the
xz plane.
Finding the x and z component of the force
is a two-step process.
First, we find the projection of the force
on the xz plane using the sine value of the
angle theta.
Let us call this component of this force as
F sub xz, and its magnitude is shown here.
This is actually an intermediate value.
Once we know this component, we can easily
determine the x and z components of the force
using the angle phi as shown here.
As you can see this is an effective approach
if you know two angles.
Various problems may have slightly different
information available, but you should be able
to determine the components, once you have
a good understanding of what is given.
In case of our flower pot, for simplicity
let us say, the angle between the vertical
line and each rope force is the same, and
it is theta sub y.
The angle between the projection of force
F1 on xz plane is phi.
With this information, you can easily find
x and z component of the force as we just
did before.
