pre calculus
posted by Meredith .
in the equation (x4)^2+y^2=16 the letters x and y represent rectangular coordinates. Write the equivalent equation using polar coordinates. solve for r

pre calculus 
Reiny
from your previous question, recall
sinØ = y/r > y = rsinØ
cosØ = x/r > x = rcosØ
(x4)^2+y^2=16
(rcosØ 4)^2 + r^2sinØ = 16
r^2 cos^2  8rcosØ + 16 + r^2sin^2 Ø = 16
r^2 (cos^2 Ø + sin^2 Ø)  rcosØ + 16 = 16
r^2 rcosØ = 0
r  cosØ = 0
check:
http://www.wolframalpha.com/input/?i=polar+plot+r+%3D+cos%C3%98
http://www.wolframalpha.com/input/?i=plot+(x4)%5E2%2By%5E2%3D16 
pre calculus 
Steve
Clearly the graph is a circle of radius 4 with center at (4,0).
You know that r = cosθ is a circle with radius 1/2 and center at (0,1/2).
so, we have r = 8cosθ 
pre calculus 
Reiny
Steve has the correct equation.
I don't know why my 8 was dropped in my 3rd last line, just careless.
Respond to this Question
Similar Questions

Polar to Rectangular Form
The letters r and theta represent polar coordinates. Write each equation in rectangular coordinates (x, y) form. Let t = theta (1) r = sin(t) + 1 (2) r = sin(t)  cos(t) 
Write in (x , y) Form
The letters r and theta represent polar coordinates. Write each equation in rectangular coordinates (x, y) form. (1) r = 4 (2) r = 3/(3  cos(t)), where t = theta 
Precalculus
The letters r and è represent polar coordinates. Write the equation using rectangular coordinates (x,y). r=1+2sinè I know that I have to use something along the lines of x=rcosè and y=rsinè, but I'm stuck when I try to figure it … 
pre calc.Math
Please help me any one of these please! Thank You to any one r=26 cos(θ) convert this polar coordinate equation into an equation in rectangular coordinates(x,y) given (8,8) convert this point into polar coordinates with 6 >= … 
Math ! Please Help !
1.Graph the polar equation r=32sin(theta) 2. Find the polar coordinates of 6 radical 3,6 for r > 0. 3. Find the rectangular coordinates of (7, 30°). 4. Write the rectangular equation in polar form. (x – 4)2 + y2 = 16 5. Write … 
Calculus please help !
1.Graph the polar equation r=32sin(theta) 2. Find the polar coordinates of 6 radical 3,6 for r > 0. 3. Find the rectangular coordinates of (7, 30°). 4. Write the rectangular equation in polar form. (x – 4)2 + y2 = 16 5. Write … 
Precalculus; urgent ! Please help !
1.Graph the polar equation r=32sin(theta) 2. Find the polar coordinates of 6 radical 3,6 for r > 0. 3. Find the rectangular coordinates of (7, 30°). 4. Write the rectangular equation in polar form. (x – 4)2 + y2 = 16 5. Write … 
Pre calculus
Find the rectangular equation for the given polar coordinates: R=(7/(5+4sin theta)) 
Trig (math)
1.) Find all solutions of the equation. Leave answers in trigonometric form. x^2 + 1  sqrt3i = 0 2.) Give the rectangular coordinates for the point. (9, 2pi/3) 3.) The rectangular coordinates of a point are given. Express the point … 
Pre calculus
in the equation r= 5/(sin theta +2cos theta) the letters r and theta represent polar coordinates. Write the equivalent equation using rectangular coordinates. Thanks :)