SOLUTION: I need to find a rectangular equation equivalent to r = cos(theta) A) x^2 + y^2 = x B) x^2 + y^2 = y C) x^2 - y^2 = x D) x^2 - y^2 = y E) None of these I must be doing some

Algebra ->  Trigonometry-basics -> SOLUTION: I need to find a rectangular equation equivalent to r = cos(theta) A) x^2 + y^2 = x B) x^2 + y^2 = y C) x^2 - y^2 = x D) x^2 - y^2 = y E) None of these I must be doing some      Log On


   

Question 121066: I need to find a rectangular equation equivalent to r = cos(theta)
A) x^2 + y^2 = x
B) x^2 + y^2 = y
C) x^2 - y^2 = x
D) x^2 - y^2 = y
E) None of these
I must be doing something wrong as I am not getting any fo these and am fairly sure the answer isn't E. Thank you!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Using the conversion formulas that convert polar to rectangular, we have




and






Now square both sides of the second formula


------------------

Now let's manipulate :


Multiply both sides by r


Replace with . Remember,



Replace with . Remember,



So the polar equation converts to

So the answer is A)


Check:
You can graph the original equation and . You'll see that they trace out the same circle.