Calculus BC Summer Work Assignment 4 Polar and Parametrics
Polar Coordinates Review
1) Graph a point with the given polar coordinates:
a) (2, π )
b) −1, 3π
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c)
(3, -45°)
2) Find the rectangular coordinates for each point given in polar coordinates:
a) 1.5, 7π
b) ( −2, π )
c) ( 2, 270°)
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3) Rectangular coordinates of point P are given. Find all polar coordinates that
satisfy 0 ≤ θ ≤ 4π .
a) P= (1,1)
b) P=(1,3)
c) P= (-2, 5)
4) For each of the following, convert the polar equation to rectangular form and
identify the graph.
a) r = 3sec θ
b) r = −3sin θ
c) r csc θ = 1
5) Convert the rectangular equation to polar form.
a) x=2
b) 2 x − 3 y = 5
c) ( x − 3) + y 2 = 9
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6) The location, given in polar coordinates of two planes approaching the Dayton
Airport are (4mi, 12°) and (2mi, 72°). Find the distance between the 2 airplanes.
7) A square with sides length a and center at the origin has 2 sides parallel to the xaxis. Find the polar coordinates of the vertices.
Parametrics:
1) Find a rectangular equation for the plane curve defined by the following
parametric equations:
a) x = 3t , y = t + 7
b) x = t , y = t 2 + 5
c) x = sin θ , y = 3cos θ
2) Find parametric equations for the rectangular equations:
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a). y = 3x − 4
b) ( x − 2) + ( y − 4) = 4
3) Mike throws a ball straight up with an initial speed of 60ft/sec from a height of 3
feet. Find parametric equations that describe the motion of the ball as a function of
time. How long is the ball in the air? When is the ball at its maximum height. What is
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its max heighth? ( − gt 2 + vot + ho )-might be helpful.
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