trig - rectangular coordinates?

Question

how do you write the equation with rectangular coordinates?

r²= 4cos2θ

Answer 1

r²= 4cos2θ
put x = rcosθ
y = rsinθ
=> r² = r² (cos² θ + sin² θ) = x² + y² = 4cos2θ =
4(2cos² θ -1) = 4(2(x²/(x² + y²)) -1)
Because we know that cos² θ = x²/ r² and r² = x² + y²

so the eqn becomes :
x² + y² = 4(2(x²/(x² + y²)) -1)
or (x² + y²)² = 8x² - 4(x² + y²)
or x^4 + y^4 + 2x²y² - 4x² + 4y² = 0

Answer 2

If I'm not mistaken you are trying to convert polar to rectangular. Rectangular has a real numbers axis (X) and an imaginary numbers axis (Y) whereas polar is a magnitude (Z) and an angle (Theda). The R to P conversion is:
Z=(X^2+Y^2)^0.5 and Theda=(Tangent Y)/X. The P to R conversion is: X=Z/Cosine Theda and Y=Z/Sine Theda. I don't know where you got your formula, so I may be wrong in understanding what the question is you are asking.

Answer 3

r² = x² + y²
and
cos 2x = 2cos²x - 1 = 2(x/r)² - 1 = 2x²/r² - 1

r² = 4(2x²/r² - 1)
r² = 8x²/r² - 4
If we multiply the equation by r², you get:

r^4 = 8x² - 4r²
Now substitute r² = x² + y²
(x² + y²)² = 8x² - 4x² - 4y²

It's not all that pretty, but it is rectangular. By the way, that is the graph of a lemniscate, which looks like the infinity symbol.

Answer 4

1500 COORDINATES!!!


To join the coordinates the program Google Earth, first we must copy the coordinates, and them to go with the option FLY TO of the Google Earth


http://ar.geocities.com/coordenadasgoogle/coordinates.html


Bless!!!

Answer 5

polar coordinates are expressed as (r, theta). accordingly, r = -a million theta = - 7pi/6 theta will be typed T. -7pi/6 is coterminal with 5pi/6 x = r*cos T & y = r* sin T x = -a million*cos (-7pi/6) & y = -a million* sin (-7pi/6) x = -a million*cos(5pi/6) & y = -a million* sin (5pi/6) x = -a million*-sqrt3/2 & y = -a million* a million/2 rectangular coordinates (x,y) = ( sqrt3/2, -a million/2)