Calculus Volume 3 · free preview
Polar Coordinates
Polar coordinates locate points by distance and angle from the origin, converting to and from Cartesian coordinates, and polar curves r equals f of theta include circles, cardioids, and roses with rich symmetry.
1. The polar coordinate system
The polar coordinate system
2. Standard polar curves
Standard polar curves
3. Symmetry and plotting economy
Symmetry and plotting economy
4. Converting polar and Cartesian equations
Converting polar and Cartesian equations
5. Conversion to Cartesian
The polar point (2, pi/3) has which Cartesian coordinates?
6. Negative r meaning
In polar coordinates, what does a negative r value indicate?
7. Rose petal count
The rose r = cos(3 theta) has how many petals?
8. Circle through origin
The polar equation r = 2 cos theta describes which circle?
9. Limacon inner loop
The limacon r = a + b cos theta with a less than b exhibits which feature?
10. Pole coordinates
At the pole, r equals 0 for every angle theta. As a number, what is r? Answer with a number.
11. Cardioid symmetry
The cardioid r = 1 + cos theta is symmetric about which axis, the x axis or the y axis? Answer in lowercase.
12. Spiral unboundedness
The spiral r = theta for theta at least 0 has r growing without bound as theta grows. As one word, what is it? Answer in lowercase.
13. Theta non-uniqueness
The point (2, pi/3) is also named (2, pi/3 + 2 pi k) for any integer k. What does this demonstrate?
14. Three polar names
The point (2, pi/3) also has the name (2, 7 pi/3) and the negative-radius name (-2, 4 pi/3). As a number, how many names are listed? Answer with a number.
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