W13 Stepwise

Due date: Thursday 4/9, 11:59pm

More parametric calculus

01

06

Cycloid - Arclength and surface area of revolution

Consider the cycloid given parametrically by $c(t)=(t-\sin t,1-\cos t)$.

(a) Find the length of one arch of the cycloid.

(b) Suppose one arch of the cycloid is revolved around the $x$-axis. Find the area of this surface of revolution.

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Solution

Solutions---0260-06

Polar curves

02

01

Convert points: Cartesian to Polar

Convert the Cartesian (rectangular) coordinates for these points into polar coordinates:

(a) $(\mathrm{1,0})$ $$ (b) $(3,\sqrt{3})$ $$ (c) $(-\mathrm{2,2})$ $$ (d) $(-1,\sqrt{3})$

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Solution

Solutions---0270-01

03

02

Convert equations: Polar to Cartesian

Convert the polar equation to a Cartesian equation. Be sure to simplify.

(a) $r=7$ $$ (b) $r=2\sin \theta$ $$ (c) $r={\displaystyle \frac{1}{\cos \theta -\sin \theta }}$

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Solution

Solutions---0270-02