Polar Test

NON-CALCULATOR

_____ 1. Which of the following would graph a point in quadrant III? I. (-4, -5π/3) II. (4, 16π/3) III. (-4, 4π/3)

a. I b. II c. III d. I & II e. II & III f. none

_____ 2. Which statement is true?

a. Converting the point (6, 5π/6) to a rectangular coordinate is (-3, 3√3) b. One polar name for the point (-2, -2) is ( 2√2, π/4) c. One polar name for the point (-1, √3) is (-2, -π/3) d. Converting the point (-6, 15π/4) to a rectangular coordinate is (-3√2, -3√2) e. No statements are true.

_____ 3. All of the following polar coordinates represent the rectangular coordinate (1/2, -√3/2) EXCEPT:

a. (1, 660°) b. (1, -60°) c. (-1, 120°) d. (-1, -240°) e. (-1, -420°)

_____ 4. Which of the following graphs would have points in all four quadrants?

I. r = 2 – 2 cos θ II. r = 4 cos θ III. r = 3θ

a. I b. II c. III d. I & II e. I & III f. I, II & III

_____ 5. Which graph possesses both of the characteristics: symmetric about the y-axis and contains the pole?

a. r = 6 cos 2θ b. r = 3 + 2 sin θ c. r = 1 + 3 cos θ d. both a & b e. none of them

_____ 6. Which of the following does NOT graph a circle?

a. r = 2 b. r csc θ = 7 c. r = -4 cos θ d. r = 5 sec θ e. all graphs circles

_____ 7. When drawing the graph of r = -3 sin 2θ, in which order do the quadrants get graphed?

a. I, II, II, IV b. II, IV, I, II c. III, I, II, IV d. III, II, I, IV

_____ 8. Changing the equation 4x – 5y = 7 to a polar equation would yield:

a. r = 7 b. r = 7 c. r = 7 d. r = 7 4cosθ + 5sinθ 4cosθ - 5sinθ 4sinθ – 5cosθ 4sinθ + 5cosθ

_____ 9. Change the equation r = 3 to a rectangular equation.