Module 25 - Parametric Equations

Module 25 - Answers

Lesson 1

Answer 1

25.1.1 The arches of the cycloid are higher and wider.

Answer 2

25.1.2 The radius of the tire is a units.

Answer 3

25.1.3

After 7 revolutions the reflector appears to return to its starting point.

Lesson 2

Answer 1

25.2.1

At t = 0.5

dy/dt 1.2984

and

dx/dt 0.6225.

These values satisfy the Chain Rule since , which is the previously found value for dy/dx.

Answer 2

25.2.2

The line tangent to the curve when t = 2 is y = 0.6421(x - 1.0907) + 1.4161.

Lesson 3

Answer 1

25.3.1 The arc length for

is about 1.5 units.

Answer 2

25.3.2 The length of the spiral of Archimedes between t = 0 and t = 10 is about 51.748 units.

Self Test

Answer 1

Answer 2

Answer 3

Answer 4

The tangent line to the curve at

is y = 0.5(x + 0.5) - 0.5.

Answer 5

The length of the curve between t = 0 and

is about 3.341 units.