Chapter 10: Q. 44 (page 695)

In Problems 43 and 44, the parametric equations of four curves are given. Graph each of them, indicating the orientation.
$C_{1} : x = t, y = \sqrt{1 - t^{2}}, - 1 \leq t \leq 1 C_{2} : x = \sin t, y = \cos t, 0 \leq t \leq 2 π C_{3} : x = \cos t, y = \sin t, 0 \leq t \leq 2 π C_{4} : x = \sqrt{1 - t^{2}}, y = t, - 1 \leq t \leq 1$

Short Answer

Expert verified

The graph of each figure is shown in respective figures.

Step by step solution

Step 1. Given Information

The given parametric equations are

$C_{1} : x = t, y = \sqrt{1 - t^{2}}, - 1 \leq t \leq 1 C_{2} : x = \sin t, y = \cos t, 0 \leq t \leq 2 π C_{3} : x = \cos t, y = \sin t, 0 \leq t \leq 2 π C_{4} : x = \sqrt{1 - t^{2}}, y = t, - 1 \leq t \leq 1$

Step 2. Graph of C1

We have $x = t, y = \sqrt{1 - t^{2}}, - 1 \leq t \leq 1$

The coordinates are $(- 1, 0), (0, 1), (1, 0)$

Plot these points on the plane and join them to obtain the graph

Step 3. Graph of C2

We have $x = \sin t, y = \cos t, 0 \leq t \leq 2 π$

The coordinates are $(0, 1), (1, 0), (0, - 1), (- 1, 0), (0, 1)$

Plot these points on the plane and join them to obtain the graph

Step 4. Graph of C3

We have $x = \cos t, y = \sin t, 0 \leq t \leq 2 π$

The coordinates are $(1, 0), (0, 1), (- 1, 0), (0, - 1), (1, 0)$

Plot these points on the plane and join them to obtain the graph

Step 4. Graph of C4

We have $x = \sqrt{1 - t^{2}}, y = t, - 1 \leq t \leq 1$

Plot these points on the plane and join them to obtain the graph

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Short Answer

Step by step solution

Step 1. Given Information

Step 2. Graph of C1

Step 3. Graph of C2

Step 4. Graph of C3

Step 4. Graph of C4

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In Problems 43 and 44, the parametric equations of four curves are given. Graph each of them, indicating the orientation.C1:x=t,y=1-t2,-1≤t≤1C2:x=sint,y=cost,0≤t≤2πC3:x=cost,y=sint,0≤t≤2πC4:x=1-t2,y=t,-1≤t≤1

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Graph of C1

Step 3. Graph of C2

Step 4. Graph of C3

Step 4. Graph of C4

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Pure Maths

Probability and Statistics

Calculus

Geometry

Statistics

Study anywhere. Anytime. Across all devices.