1. r = 6/(2-3sinθ)
2. r = 4/(7-7sinθ)
2007-05-29 14:29:33 · 3 answers · asked by ohyeah 1 in Science & Mathematics ➔ Mathematics
Use these rules to determine your X and Y values
x = r cos(n)
y = r sin(n)
r^2 = x^2 + y^2
n = arctan(y/x)
2007-05-29 14:39:07 · answer #1 · answered by JR 1 · 0⤊ 0⤋
Remember the identities.
x = rcosθ
y = rsinθ
x² + y² = r²
1. r = 6/(2 - 3sinθ)
r(2 - 3sinθ) = 6
2r - 3rsinθ = 6
2r - 3y = 6
2r = 6 - 3y
Square both sides.
4r² = 36 - 36y + 9y²
4x² + 4y² = 36 - 36y + 9y²
4x² - 5y² + 36y = 36
4x² - 5(y² - (36/5)y) = 36
4x² - 5(y² - (36/5)y + 324/25) = 36 - 5(324/25)
4x² - 5(y - 18/5)² = -144/5
5(y - 18/5)² - 4x² = 144/5
(y - 18/5)²/(144/25) - x²/(36/5) = 1
2007-05-29 16:01:43 · answer #2 · answered by Northstar 7 · 0⤊ 0⤋
1. r = 6/(2-3sin8) ~ 1
2. r = 4/(7-7sin8) ~ 8
2007-05-29 14:41:58 · answer #3 · answered by a.michaellewis 1 · 0⤊ 0⤋