Graph the parametric equations, indicate the direction of the curve on the graph.?

Question

x = 5sint
y = 1+2cost
(use radians for the values of t)

Find all x and y values for each t value.

Graph at :
http://i49.photobucket.com/albums/f263/aubreybruin/xy-graph2.gif

Answer 1

ellipse drawn clockwise from 12 o'clock

Answer 2

We have the parametric equations.

x = 5sint
y = 1+2cost

x/5 = sint
(y - 1)/2 = cost

(x/5)² + [(y - 1)/2]² = sin²t + cos²t

x²/25 + (y - 1)²/4 = 1

This is the equation of an ellipse.

For t = 0, (x,y) = (0,3)
For t = π/2, (x,y) = (5,1)
For t = π, (x,y) = (0,-1)
For t = 3π/2, (x,y) = (-5,1)

The direction of the curve is clockwise starting from
12 o'clock.

Answer 3

a) x = 3cos(t/2) x^2 = 9cos^2(t/2) -----------(1) y = 6 sin(t/2) divide by 2 (1/2)y = 3 sin(t/2) (1/4)y^2 = 9 sin^2(t/2) (1/4)y^2 = 9 (1 - cos^2(t/2)) (1/4)y^2 = 9 - 9cos^2(t/2) substitute 9 cos^2(t/2) = x^2 from (1) (1/4)y^2 = 9 - x^2 => y^2 = 36 - 4x^2 b) at t = π/2 x = 3cos(π/4) = 3/√2 = (3√2)/2 y = 6 sin(π/4) = 6/√2 = 3√2 at t = π x = 3cos(π/2) = 0 y = 6sin(π/2) = 6 at t = 3π/2 x = 3cos(3π/4) = - (3√2)/2 y = 6sin(3π/4) = 3√2 The three points are (x, y) = ((3√2)/2, 3√2), (0, 6) and (-(3√2)/2, 3√2)