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Step 1 - Label sides
The first step is to label the sides of the right-triangle
that our vector creates with the x-axis. Remember from
basic trigonometry that the side opposite over the hypotenuse is
called the sine of the angle. The side adjacent over the
hypotenuse is called the cosine of the angle. Once we know
this it's easy to convert from polar coordinates to cartesian
coordinates.
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Step 2 - Remember some basic Trig
Recall from basic trig that the side opposite over the
hypotenuse is called the sine of the angle. Similarly, the
side adjacent over hypotenuse is called the cosine of the angle.
We can use these formulas to calculate the x and y components of
the vector.
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Step 3 - Calculate x
Looking at the formulas for sine and cosine it should be
apparent that the x-component of the vector is simply the length
of the side adjacent. The length of the vector is just the
length of the hypotenuse. Using this knowledge we can
calculate x.
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Step 4 - Calculate y
The y-component formula is derived in a similar fashion as
shown.
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