Unformatted text preview: θ) and r = 2 − 2 sin(θ) intersect when θ = π . Hence, for the
6
ﬁrst region, (r, θ) : 0 ≤ r ≤ 2 sin(θ), 0 ≤ θ ≤ π , we are shading the region between the origin
6
(r = 0) out to the circle (r = 2 sin(θ)) as θ ranges from 0 to π , which is the angle of intersection
6
of the two curves. For the second region, (r, θ) : 0 ≤ r ≤ 2 − 2 sin(θ), π ≤ θ ≤ π , θ picks
6
2
up where it left oﬀ at π and continues to π . In this case, however, we are shading from the
6
2
origin (r = 0) out to the cardioid r = 2 − 2 sin(θ) which pulls into the origin at θ = π . Putting
2
these two regions together gives us our ﬁnal answer.
y y 1 θ= 1 π
6 1 r = 2 − 2 sin(θ) and r = 2 sin(θ ) x 1 x (r, θ) : 0 ≤ r ≤ 2 sin(θ), 0 ≤ θ ≤ π ∪
6
(r, θ) : 0 ≤ r ≤ 2 − 2 sin(θ), π ≤ θ ≤ π
6
2 816 Applications of Trigonometry 11.5.1 Exercises 1. Plot the graphs of the following polar equations by hand. Carefully label your graphs.
(a) Circle: r = 6 sin(θ) (j) Cardioid: r = 5 + 5 sin(θ) (b) Circle: r = 2 cos(θ) (k) Cardioid: r = 2 + 2 c...
View
Full Document
 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

Click to edit the document details