# pre calculus

in the equation (x-4)^2+y^2=16 the letters x and y represent rectangular coordinates. Write the equivalent equation using polar coordinates. solve for r

1. from your previous question, recall
sinØ = y/r --> y = rsinØ
cosØ = x/r --> x = rcosØ

(x-4)^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+(x-4)%5E2%2By%5E2%3D16

posted by Reiny
2. 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

posted by Steve
3. Steve has the correct equation.
I don't know why my 8 was dropped in my 3rd last line, just careless.

posted by Reiny

## Similar Questions

1. ### 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 :)
2. ### 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
3. ### 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
4. ### 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
5. ### 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)

1.Graph the polar equation r=3-2sin(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.