W14 Stepwise

Due date: Thursday 4/16, 11:59pm

Polar calculus

01

01

Polar curve - Vertical or horizontal tangent lines

Find all points on the given curve where the tangent line is horizontal or vertical.

$$r=\cos \theta \theta \in [0,2\pi )$$

Hint: First determine parametric Cartesian coordinate functions using $\theta$ as the parameter.

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Solution

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Polar curves

02

06

Sketching roses

Sketch the graphs of the following polar functions.

Use numbers to label the order in which the leaves/loops are traversed.

(a) $r=\sin 2\theta$ (b) $r=\sin 3\theta$ (c) $r=2\cos 2\theta$

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Solution

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03

04

Polar coordinates - lunar areas

(a) Find the area of the yellow region.

(b) Find the area of the green region.

(You can find these in either order.)

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Solution

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