finish the chart and graph it please ### Parametric Equations and Elimination of Parameters#### Given Parametric Equations:- $ x = 3 \cos t - 3 $- $ y = 3 \sin t + 1 $- Interval: $ 0 \leq t \leq 2\pi $#### Table of Values:| $ t $ | $ x $ Calculation | $ y $ Calculation | $ (x, y) $ ||-----------|----------------------------------|--------------------------------|--------------|| 0 | $ 3 \cos(0) - 3 = 0 $ | $ 3 \sin(0) + 1 = 1 $ | $ (0, 1) $ || $\pi/4$ | $ 3 \cos(\pi/4) - 3 = 3\sqrt{2}/2 - 3 $ | $ 3 \sin(\pi/4) + 1 = 3\sqrt{2}/2 + 1 $ | | | $\pi/2$ | | | || $3\pi/4$| | | || $\pi$ | | | || $5\pi/4$| | | || $3\pi/2$| | | || $7\pi/4$| | | || $2\pi$ | | | |#### Steps to Eliminate the Parameter:To eliminate the parameter, express $ x $ and $ y $ in terms of each other without $ t $.#### Graph Explanation:The graph on the right is a coordinate plane labeled with the x-axis and y-axis. Several points derived from the table above are plotted to visualize the parametric equations' path. Each plotted point corresponds to a calculated $ (x, y) $ pair from the table. The path depicted traces out a circle due to the trigonometric sine and cosine functions with amplitudes from $ t = 0 $ to $ t = 2\pi $.Through this activity, learners will understand how parametric equations define a path in the coordinate plane and explore the relationship between trigonometric functions and circular movement.

Answered: Image /qna-images/answer/c124ea9c-596e-4a7b-8b7a-acf66fffa5f6.jpg

a) x 3cost-3, y3sint+1,0si<2a x = 3 (ost-3 y = 3smt+| 3 (os (6)-3-0 351n(0)+/= (x,y) 8TY T/4 T/2 Зп/4 3cos()-3 =0 3 sin)+1=3. Co.9,3.) 4. X. 5T/4 Зп/2 7n/4 8 -4 -2 2. 4. 6. 8 -2 2n -6 Steps for Eliminate the Parameter

a) x 3cost-3, y3sint+1,0si<2a x = 3 (ost-3 y = 3smt+| 3 (os (6)-3-0 351n(0)+/= (x,y) 8TY T/4 T/2 Зп/4 3cos()-3 =0 3 sin)+1=3. Co.9,3.) 4. X. 5T/4 Зп/2 7n/4 8 -4 -2 2. 4. 6. 8 -2 2n -6 Steps for Eliminate the Parameter

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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Question

finish the chart and graph it please

### Parametric Equations and Elimination of Parameters

#### Given Parametric Equations:
- $ x = 3 \cos t - 3 $
- $ y = 3 \sin t + 1 $
- Interval: $ 0 \leq t \leq 2\pi $

#### Table of Values:

| $ t $ | $ x $ Calculation | $ y $ Calculation | $ (x, y) $ |
|-----------|----------------------------------|--------------------------------|--------------|
| 0 | $ 3 \cos(0) - 3 = 0 $ | $ 3 \sin(0) + 1 = 1 $ | $ (0, 1) $ |
| $\pi/4$ | $ 3 \cos(\pi/4) - 3 = 3\sqrt{2}/2 - 3 $ | $ 3 \sin(\pi/4) + 1 = 3\sqrt{2}/2 + 1 $ | |
| $\pi/2$ | | | |
| $3\pi/4$| | | |
| $\pi$ | | | |
| $5\pi/4$| | | |
| $3\pi/2$| | | |
| $7\pi/4$| | | |
| $2\pi$ | | | |

#### Steps to Eliminate the Parameter:
To eliminate the parameter, express $ x $ and $ y $ in terms of each other without $ t $.

#### Graph Explanation:
The graph on the right is a coordinate plane labeled with the x-axis and y-axis. Several points derived from the table above are plotted to visualize the parametric equations' path. Each plotted point corresponds to a calculated $ (x, y) $ pair from the table. The path depicted traces out a circle due to the trigonometric sine and cosine functions with amplitudes from $ t = 0 $ to $ t = 2\pi $.

Through this activity, learners will understand how parametric equations define a path in the coordinate plane and explore the relationship between trigonometric functions and circular movement.

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