Module 25 - Answers
 
Lesson 1
 
 Answer 1
 
25.1.1   They are and where n is any integer.
 
 Answer 2
 
25.1.2  

The rectangular coordinates for the polar point (2, /3) are .

 
Lesson 2
 
 Answer 1
 
25.2.1

This is a three-leafed rose. The entire graph is plotted for , so in the Window Editor could be set to to draw the entire graph.

 
 Answer 2
 
25.2.2  

r = 3 sin(4 )

r = 3 sin(5 )

r = 3 sin(6 )

r = 3 sin(7 )

When n is even there are 2n leaves and the entire graph is plotted for . When n is odd there are n leaves and the entire graph is plotted for .

 
 Answer 3
 
25.2.3  

The graph has six overlapping leaves.

 
Lesson 3
 
 Answer 1
 
25.3.1 The area enclosed by the semicircle r = 2 on the interval is 2 square units.
 
 Answer 2
 
25.3.2 The points of intersection of the two curves are at = and = . The area inside the circle and outside the cardioid is
 
Self Test
 
 Answer 1
 
 
 Answer 2
 
 
 Answer 3
 

[0,2 ] x [–8,8] x [–4,4]

 
 Answer 4
 
y 0.892x – 0.009
 
 Answer 5
 
The arc length 21.01 units.
 
 Answer 6
 
The area of one leaf is square units.
 
 

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