Module 23  Answers  
Lesson 1  
Answer 1  
23.1.1
The values of t are restricted to nonnegative values and because x = t the values of x are also restricted to those values. 

Answer 2  
23.1.2
Swapping x and y produces the inverse relation whose graph is the original graph reflected across the line y = x.


Answer 3  
23.1.3
[0, 2 ] x [4, 4] x [2, 2] The first interval given in the window coordinates above represents tvalues, the second and third intervals represent x and yvalues, respectively. 

Answer 4  
23.1.4
The number of petals is N  1 in the epicycloid x = N sin t  sin N t y = N cos t  cos N t 

Lesson 2  
Answer 1  
23.2.1 dydx(0.5) = 2.08583, which agrees with the value found using the "Derivative" feature of the Graph screen.  
Answer 2  
23.2.2 The slope of the tangent line when t = 2 is dydx(2) 0.642093  
Answer 3  
23.2.3
The window shown is [ , ] x [3, 3] x [5, 5]. The equation of the tangent to the curve when t = 2 is y 0.642093x + 0.715815. 

Lesson 3  
Answer 1  
23.3.1 The arc length is 3/2 units.  
Self Test  
Answer 1  
Answer 2  
1/2  
Answer 3  
7/4  
Answer 4  
y = 0.5x – 0.25  
Answer 5  
3.34122 units  
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