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Chapter 9: Q. 02 (page 720)

Examples: Construct examples of the thing(s) described in the following. Try to find examples that are different than any in the reading.

(a) Parametric equations $$x = f(t), y = g(t)$$ on the interval $$[0, 1)$$ that trace the unit circle exactly once clockwise, starting at the point $$(1, 0)$$.

(b) Parametric equations $$x = f(t), y = g(t)$$ on the interval $$[0, 2蟺)$$ that trace the circle centered at $$(2, 鈭�3)$$ with radius 5 exactly once counterclockwise, starting at the point $$(7, 鈭�3)$$.

(c) Parametric equations $$x = f(t), y = g(t)$$ whose graph is not the graph of a function $$y = f(x)$$.

Short Answer

Expert verified

(a) $$(cost, -sint)$$

(b) $$(2+5cost, 5sint-3)$$

(c) $$(rcost, rsint)$$

Step by step solution

01

Step 1. Given Information

Parametric equations $$x = f(t), y = g(t)$$ on the interval $$[0, 1)$$ that trace the unit circle exactly once clockwise, starting at the point $$(1, 0)$$.

02

Step 2. Explanation

The constructed example can be given as, $$(cost, -sint)$$

03

Step 3. Given Information

Parametric equations $$x = f(t), y = g(t)$$ on the interval $$[0, 2蟺)$$ that trace the circle centered at $$(2, 鈭�3)$$ with radius 5 exactly once counterclockwise, starting at the point $$(7, 鈭�3)$$.

04

Step 4. Explanation

The constructed example can be given as, $$(2+5cost, 5sint-3)$$

05

Step 5. Given Information

Parametric equations $$x = f(t), y = g(t)$$ whose graph is not the graph of a function $$y = f(x)$$.

06

Step 6. Explanation

The constructed example can be given as, $$(rcost, rsint)$$

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