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Points, Vectors, and Functions
Home
Calculus
Points, Vectors, and Functions
Exercises
Polar Coordinates Exercises
Switching Coordinates Exercises
Intro
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Functions
Increasing or Decreasing or...
Bounded
Even and Odd Functions
Magnitude
Direction
Scaling Vectors
Unit Vectors
Vector Functions
Sketching Vector Functions
Graphing Parametric Equations
Points on Graphs of Parametric Equations
Parametrizations of the Unit Circle
Parameterization of Lines
Polar Coordinates
Simple Polar Inequalities
Switching Coordinates
Translating Equations and Inequalities between Coordinate Systems
Graphing Polar Functions
Rules of Graphing We Do (or Don't) Have
Bounds on Theta
Intersections of Polar Functions
Table of Contents
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Page (1 of 4) Exercises:
1
2
3
4
Exercise 1
Convert each set of rectangular coordinates to polar coordinates.
(1,1)
Answer
Draw the triangle for the point
We know
therefore
To find
r
we use the Pythagorean Theorem:
We conclude that the polar coordinates of this point are
Draw the triangle for the point (1,1):
We have
and
The polar coordinates of the point are
Draw the triangle for the point
We have
therefore
Using the Pythagorean theorem,
The polar coordinates of the point are
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More Switching Coordinates Exercises (2 of 4)
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Simple Polar Inequalities Exercises