Find the rectangular coordinates for each of the following polar coordinates:

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1 WORKSHEET Plot the following: 7 3 A. 6, B. 3, D. 6, 3 C., 11 2 E. 5, F. 4, 6 3 Find the rectangular coordinates for each of the following polar coordinates: , 3. 8, 6 3 Given the rectangular coordinates below, find the polar coordinates satisfying the conditions given: 3 ; r 0 and , , 5 3 ; r 0 and

2 4 ; r 0 and ,4 Change the following polar equations to rectangular equations: 7. r 8 8. r cos 6 9. r 5csc 10. r 7sin Change the following rectangular equations to polar equations: x y y y 2 10x 14. 3xy 7

3 WORKSHEET Convert to rectangular coordinates: Convert to polar coordinates: 5 1., ,4 ; r 0 and 0 2 Change the following polar equations to rectangular equations: 3. r 3sec 4. r 5cos Change the following rectangular equations to polar equations: x y x y 2 0 Identify the polar graph (circle with center at pole, circle with center on x-axis, circle with center on y-axis, line through pole, spiral out, spiral in): 7. r 4cos 8. r r r 4sin 12. r 4

4 Graph: 13. r r 6cos 16. r 4sin r r 5

5 WORKSHEET Graph: 1. r 3 3cos 2. r 4 4sin 3. r 4 6cos 4. r 7 2sin 5. r 5 3cos 6. r 3 4sin

6 WORKSHEET Identify the polar graph (circle, spiral, cardioid, limacon, rose): If a circle, name the center (in polar coordinates) and the radius. If a limacon, name the type. If a rose, state the number of petals. 1. r 4cos 2. r 5 2sin 3. r 7sin10 4. r 6 5. r 4 7sin 6. r 4 7. r 2sin 8. r 6 6cos 9. r 8cos r r 8 6cos

7 Graph: 12. r 6sin r 7cos r 8cos r 8sin 16. r 9cos r 10sin 4

8 WORKSHEET Find the area enclosed by: 1. r 8 sin 2. r 5 5cos 3. r 6sin 4 4. r 8cos 3

9 5. r 5 4cos 6. r 3 6sin 7. the inner loop of r 3 6sin 8. between the inner and outer loops of r 3 6sin

10 WORKSHEET Find the area outside of r 6sin and inside of r 6cos in the first quadrant 2. Find the area outside of r 2 2cos and inside of r 4 3. Find the area outside of r 6 and inside of r 3 6cos

11 WORKSHEET Obtain the rectangular equation by eliminating the parameter. Sketch a graph using either the parametric equations or the rectangular equation. 1. x 1 t, y 1 t 2. x 2t 5, y 4t 7 3. x 3 3t, y 2t 4. x t, y t 5. x t, y t 6. x 4 t, y t 7. x 3t, 2 y 9t 8. 2 x t, 2 y 4 t use 0 t 2 9. x 4cos, y 2sin 10. x 2sin, y 3cos x 9sin, 2 y 9cos x sec 1, y tan

12 WORKSHEET Find dy/dx in terms of the parameter. Then, find the slope and the equation of the tangent line at the given parameter. 1. x t 2 t, y t 2 t, t 1 2. x 3t, 3 y 8t, 1 t 2 3. x t 1, y 3t, t x t, y 2 ln t, t 1 5. t x 2e, 1 t y e 3, t 0 6. x t ln t, y ln t, t e 7. x 4sin, y 2cos, 8. x 2sin 2 4, y 2cos 2, 3 t 8

13 CHAPTER 13 PRACTICE TEST Convert to rectangular coordinates: Convert to polar coordinates: 5 1., , 6 3 ; r 0 and 0 2 Change to a rectangular equation: Change to a polar equation: 3. r 3cos 4. x y 2x Match the equation to the type of polar graph. 5. r 6 5cos A. line I. dimpled limacon 6. r 2sin B. circle with center at pole J. limacon with inner loop 7. r 4 C. circle with center on x-axis K. rose with 2 petals 8. r 6cos 4 D. circle with center on y-axis L. rose with 3 petals 9. r 8cos E. spiral out M. rose with 4 petals 10. r 6 2sin F. spiral in N. rose with 5 petals 11. r 8sin 3 G. cardioid O. rose with 6 petals 12. r 5 5cos H. convex limacon P. rose with 8 petals Graph: 13. r 8cos 14. r 5 5sin 15. r 6 3cos 16. r 5sin 2 Find the area: 17. enclosed by r 6 sin 18. enclosed by r 6cos enclosed by the inner loop of r 2 4cos 20. outside of r 5 and inside of r 5 4sin Obtain the rectangular equation by eliminating the parameter. 21. x 3t 7, y 6t x 3cos, 2 y 3sin Find dy/dx in terms of the parameter. Then, find the slope and the equation of the tangent line at the given parameter. 23. x 3t 2 2t, y 2t 3 1, t x 5 2ln t, 1 y 2 t, t 1

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