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Polar Coordinates Exercises
Polar Coordinate System
Mathematics 54–Elementary Analysis 2
Institute of Mathematics University of the Philippines-Diliman
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Polar Coordinates Exercises
Graphs in Polar Coordinates Special Curves in Polar Coordinates
The Polar Coordinate System
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Polar Coordinates Exercises
Graphs in Polar Coordinates Special Curves in Polar Coordinates
Polar Coordinates
Example Plot the following points:
1 2
A = (1, π/4) B = (2, −π/4)
3 4
C = (−2, π/6) D = (−3, −π/3)
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Polar Coordinates Exercises
Graphs in Polar Coordinates Special Curves in Polar Coordinates
Polar Coordinates
Example Plot the following points:
1 2
B = 2, − π = (2, 7π/4) 4
A = 1, π = (1, 9π/4) = (−1, 5π/4) 4
3 4
D = −3, − π = (3, 2π/3) 3
C = −2, π = (2, 7π/6) 6
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Polar Coordinates Exercises
Graphs in Polar Coordinates Special Curves in Polar Coordinates
Polar Coordinates
Conversion Equations Polar to Cartesian
1
Cartesian to Polar
1
x = r cos θ y = r sin θ
2
2
r 2 = x2 + y 2 y tan θ = x
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Polar Coordinates Exercises
Graphs in Polar Coordinates Special Curves in Polar Coordinates
Polar Coordinates
Example Determine the polar coordinates of the point having Cartesian coordinates (− 3, 1). Solution. Recall that r 2 = x2 + y 2 and tan θ = x . Thus, r 2 = − 3 + 12 tan θ = 1 − 3
2 y
=⇒ =⇒
r=2 θ= 5π 6
Hence, the polar coordinates are 2, 5π or −2, 11π . 6 6
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Polar Coordinates Exercises
Graphs in Polar Coordinates Special Curves in Polar Coordinates
Polar Coordinates
Example Determine the Cartesian coordinates of the point having polar coordinates −5, − π . 3 Solution. Recall that x = r cos θ and y = r sin θ. Thus, x = −5 cos − π = − 5 3 2 y = −5 sin − π = 3
5 3 2
Hence, the Cartesian coordinates are − 5 , 5 2 3 . 2
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Polar Coordinates Exercises
Graphs in Polar Coordinates Special Curves in Polar...