SOLUTION: I don't understand how my book comes up witht these answers: If anyone can help, I'd greatly appreciate it! Convert from polar equation to rectangular equation: Number 1 r=4

Draw this picture which defines x,y,r, and q
and all their relationships.





Clear of fractions:



Replace any trig functions:

Refer to the picture above and you can see that you can 
replace  by 





Now replace the r by using the Pythagorean theorem 
from the picture above.



Isolate the radical term:



Square both sides:











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Also, this one...they ask to change it to a polar equation.



Refer to the picture above, write the expressions for the sine and
the cosine:

,  

Solve for x and y:

,  

Substitute these:





Factor out  on the left



Now we can recognize that what's in the parentheses is the right side 
of the identity  which you
should have memorized. So substituting:





Replace the  by 



Invert and multiply:



Edwin