it says i also have to identify the curve x=3sin(sigma) y=4cos(sigma) rectangular equation?
H hgaon001 New member Joined May 17, 2009 Messages 39 Aug 3, 2009 #1 it says i also have to identify the curve x=3sin(sigma) y=4cos(sigma) rectangular equation?
B BigGlenntheHeavy Senior Member Joined Mar 8, 2009 Messages 1,577 Aug 4, 2009 #2 x = 3sin(θ), x2 = 9sin2(θ), sin2(θ) = x29.\displaystyle x \ = \ 3sin(\theta), \ x^{2} \ = \ 9sin^{2}(\theta), \ sin^{2}(\theta) \ = \ \frac{x^{2}}{9}.x = 3sin(θ), x2 = 9sin2(θ), sin2(θ) = 9x2. y = 4cos(θ), y2 = 16cos2(θ). cos2(θ) = y216.\displaystyle y \ = \ 4cos(\theta), \ y^{2} \ = \ 16cos^{2}(\theta). \ cos^{2}(\theta) \ = \ \frac{y^{2}}{16}.y = 4cos(θ), y2 = 16cos2(θ). cos2(θ) = 16y2. Ergo, x29 + y216 = sin2(θ) + cos2(θ) = 1, an ellipse.\displaystyle Ergo, \ \frac{x^{2}}{9} \ + \ \frac{y^{2}}{16} \ = \ sin^{2}(\theta) \ + \ cos^{2}(\theta) \ = \ 1, \ an \ ellipse.Ergo, 9x2 + 16y2 = sin2(θ) + cos2(θ) = 1, an ellipse.
x = 3sin(θ), x2 = 9sin2(θ), sin2(θ) = x29.\displaystyle x \ = \ 3sin(\theta), \ x^{2} \ = \ 9sin^{2}(\theta), \ sin^{2}(\theta) \ = \ \frac{x^{2}}{9}.x = 3sin(θ), x2 = 9sin2(θ), sin2(θ) = 9x2. y = 4cos(θ), y2 = 16cos2(θ). cos2(θ) = y216.\displaystyle y \ = \ 4cos(\theta), \ y^{2} \ = \ 16cos^{2}(\theta). \ cos^{2}(\theta) \ = \ \frac{y^{2}}{16}.y = 4cos(θ), y2 = 16cos2(θ). cos2(θ) = 16y2. Ergo, x29 + y216 = sin2(θ) + cos2(θ) = 1, an ellipse.\displaystyle Ergo, \ \frac{x^{2}}{9} \ + \ \frac{y^{2}}{16} \ = \ sin^{2}(\theta) \ + \ cos^{2}(\theta) \ = \ 1, \ an \ ellipse.Ergo, 9x2 + 16y2 = sin2(θ) + cos2(θ) = 1, an ellipse.
