PreCalculus: Chapter 9 Test Review
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1 Name: Class: Date: ID: A PreCalculus: Chapter 9 Test Review Short Answer 1. Plot the point given in polar coordinates. 3. Plot the point given in polar coordinates. (-4, -225 ) 2. Plot the point given in polar coordinates. 4. The polar coordinates of a point are given. Find the rectangular coordinates of the point. 5. The polar coordinates of a point are given. Find the rectangular coordinates of the point. (-3, -135 ) 6. The rectangular coordinates of a point are given. Find polar coordinates for the point. (0, -4) 7. The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, θ). x 2 = 3y 1
2 Name: ID: A 8. The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, θ). 13. Plot the complex number in the complex plane i 2xy = 1 9. The letters r and θ represent polar coordinates. Write the equation using rectangular coordinates (x, y). r = sin θ 10. The letters r and θ represent polar coordinates. Write the equation using rectangular coordinates (x, y). r = 10 sin θ 11. The letters r and θ represent polar coordinates. Write the equation using rectangular coordinates (x, y). 14. Plot the complex number in the complex plane i r = 2(sin θ - cos θ) 12. Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. r = 2 sin θ 15. Write the complex number in polar form. Express the argument in degrees, rounded to the nearest tenth, if necessary. - i 16. Write the complex number in polar form. Express the argument in degrees, rounded to the nearest tenth, if necessary. -5 2
3 Name: ID: A 17. Write the complex number in rectangular form Write the complex number in rectangular form. 4(cos i sin 300 ) 19. Find zw or as specified. Leave your answer in polar form. z = 10(cos 30 + i sin 30 ) w = 5(cos 10 + i sin 10 ) Find zw. 23. Find zw or as specified. Leave your answer in polar form. z = 1 + i w = - i Find zw. 24. Find zw or as specified. Leave your answer in polar form. z = 1 - i w = 1 - i Find. 20. Find zw or as specified. Leave your answer in polar form. z = 5(cos 35 + i sin 35 ) w = 2(cos 40 + i sin 40 ) Find zw. 25. Write the expression in the standard form a + bi Write the expression in the standard form a + bi. 21. Find zw or as specified. Leave your answer in polar form. z = 6 w = 12 Find zw. 22. Find zw or as specified. Leave your answer in polar form. z = 27. Write the expression in the standard form a + bi. (- + i) Find all the complex roots. Leave your answers in polar form with the argument in degrees. The complex fourth roots of Find all the complex roots. Leave your answers in polar form with the argument in degrees. The complex fifth roots of -2i 4 w = Find. 3
4 Name: ID: A 30. Use the vectors in the figure below to graph the following vector. 31. Use the vectors in the figure below to graph the following vector. u + z v - w 4
5 Name: ID: A 32. Use the vectors in the figure below to graph the following vector. 35. The vector v has initial point P and terminal point Q. Write v in the form ai + bj; that is, find its position vector. P = (3, 3); Q = (-2, -5) 36. Find the indicated quantity. Find u - v given u = -2i - 2j and v = 7i + 7j. 37. Find the indicated quantity. 2u - z - w If v = 3i - 5j and w = -7i + 4j, find 3v - 4w. 38. Find the indicated quantity. If v = -i - j, find. 39. Find the quantity if v = 5i - 7j and w = 3i + 2j Find the quantity if v = 5i - 7j and w = 3i + 2j. 33. Use the figure below. Determine whether the given statement is true or false. 41. Find the unit vector having the same direction as v. v = -3j A + H = F 34. Use the figure below. Determine whether the given statement is true or false. 42. Find the unit vector having the same direction as v. v = -4i - 3j A + B + C + D + E = 0 5
6 PreCalculus: Chapter 9 Test Review Answer Section SHORT ANSWER 1. ANS: 2. ANS: 1
7 3. ANS: 4. ANS: 5. ANS: 6. ANS: 7. ANS: r cos 2 θ = 3 sin θ 8. ANS: r 2 sin 2θ = 1 9. ANS: x 2 + y 2 = + 2y 2
8 10. ANS: x 2 + y 2 = 10y 11. ANS: x 2 + y 2 = 2y - 2x 12. ANS: x 2 + (y - 1) 2 = 1; circle, radius 1, center at (0, 1) in rectangular coordinates 13. ANS: 3
9 14. ANS: 15. ANS: 2(cos i sin 330 ) 16. ANS: 5(cos i sin 180 ) 17. ANS: 4 + 4i 18. ANS: 2-2 i 19. ANS: 50(cos 40 + i sin 40 ) 20. ANS: 10(cos 75 + i sin 75 ) 21. ANS: 72 4
10 22. ANS: 23. ANS: 2 (cos 15 + i sin 15 ) 24. ANS: (cos 15 + i sin 15 ) 25. ANS: i 26. ANS: ANS: ANS: 2(cos 45 + i sin 45 ), 2(cos i sin 135 ), 2(cos i sin 225 ), 16(cos i sin 315 ) 29. ANS: (cos 54 + i sin 54 ), (cos i sin 126 ), (cos i sin 198 ), (cos i sin 270 ), 5
11 30. ANS: 31. ANS: 32. ANS: 33. ANS: True 6
12 34. ANS: True 35. ANS: v = -5i - 8j 36. ANS: -9i - 9j 37. ANS: 37i - 31j 38. ANS: 39. ANS: ANS: 41. ANS: u = -j 42. ANS: u = - i - j 7
The polar coordinates of a point are given. Find the rectangular coordinates of the point. 1) 7, 2 3 D) - 7 2, A) - 7 2, 7 3
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