Stepwise problems - Sun. Nov 23, 11:59pm
Polar curves
01
01
Link to originalConvert points: Cartesian to Polar
Convert the Cartesian (rectangular) coordinates for these points into polar coordinates:
(a)
(b) (c) (d)
Solution
02
02
Link to originalConvert equations: Polar to Cartesian
Convert the polar equation to a Cartesian equation. Be sure to simplify.
(a)
(b) (c)
Solution
Calculus with polar curves
03
01
Link to originalPolar curve - Vertical or horizontal tangent lines
Find all points on the given curve where the tangent line is horizontal or vertical.
Hint: First determine parametric Cartesian coordinate functions using
as the parameter.
Solution
Regular problems - Sun. Nov 30, 11:59pm
Polar curves
05
03
Link to originalConvert points: Polar to Cartesian
Convert the polar coordinates for these points into Cartesian (rectangular) coordinates:
(a)
(b) (c) (d)
Solution
06
04
Link to originalConvert equations: Cartesian to Polar
Convert the Cartesian equation to a polar equation. Be sure to simplify.
(a)
(b) (c)
Solution
07
05
Link to originalSketching limaçons
Sketch the graphs of the following polar functions:
(a)
(b) (c)
(d)
Solution
08
06
Link to originalSketching roses
Sketch the graphs of the following polar functions. Use numbers to label the order in which the leaves/loops are traversed.
(a)
(b) (c)
Solution
Calculus with parametric curves
09
05
Link to originalMinimum speed of a particle
Suppose a travelling particle has position modelled by the parametric curve:
What is the slowest speed of the particle?
Solution
10
06
Link to originalCycloid - Arclength and surface area of revolution
Consider the cycloid given parametrically by
. (a) Find the length of one arch of the cycloid.
(b) Suppose one arch of the cycloid is revolved around the
-axis. Find the area of this surface of revolution.
Solution