I imagine it as a larger circle around a smaller circle. The shaded region they are referring to would be the area enclosed by the two circles. The given angle...according to my interpretation...is between the 0 degree line and the radii extending from point A.
We know the area of a circle as:
https://dl.dropbox.com/u/4645835/MATH/Area%20of%20Circle.gif
Part B:
We want to find the area of the shaded portion. So, we find the area of the outside circle and subtract from it the area of the inside circle...
Relevant Equations:
http://www.sosmath.com/trig/douangl/douangl.html
Using the given identities, I was able to simply the given equation to:
[PLAIN]https://dl.dropbox.com/u/4645835/MATH/simple.gif
I think your angle may be wrong as well. This is what I did:
[PLAIN]https://dl.dropbox.com/u/4645835/MATH/Ex1.gif
I can explain why I added 180 degrees to the angle I calculated - if needed.
Ok first off:
I believe you've recorded your answer in exponential form.
Forms of Complex Numbers:
[PLAIN]https://dl.dropbox.com/u/4645835/MATH/ComplexForms.gif
Please correct me if I'm wrong.
It is possible for an expression to fit into more than one category or into none of the categories. I'm not sure how this works anymore..as I did this a long time ago. But I think S satisfies exponential and cartesian.