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Parametric curves

(10 points) Sketch both parametric curves below. Then determine if they intersect. If
they intersect, find the point (x, y) of intersection.
C1 : x1(t) = 3 cos t,
y1(t) = 3 sin t
C2 : x2(t) = 4 sin t,
y2(t) = 4 sin t
(10 points) Plot and label the following polar points (r, θ) in the xy-plane.
(a) A = (−1, 5π/4)
(b) B = (2, 3π)
(c) C = (−2, 4π/3)
(d) D = (3, −4) [remember this point is in polar coordinates]
(10 points) Sketch the set of points (r, θ) that satisfy the following conditions:
{(r, θ) : −2 ≤ r < 2, 0 ≤ θ ≤ π/4}
(10 points) Consider the polar curve r = sin(3θ). Sketch this polar curve on the interval
2π/3 ≤ θ ≤ π.
(10 points) Use Gauss-Jordan elimination to solve the system
5x + 7y = −11
2x + y = 1
Make sure you create the augmented matrix and write down all of your elementary row operations.

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