Trigonometry and Polar Coordinates Practice Test

Review the following concepts if needed:

• The Polar Coordinate Plane Help
• Examples of Polar Coordinates Help
• Compression and Conversion Help
• The Navigator’s Way Help

Polar Coordinates Practice Test

A good score is eight correct.

1. The equal-radius axes in the mathematician’s polar coordinate system are

(a) rays

(b) lines

(c) circles

(d) spirals

2. Suppose a point has the coordinates ( θ , r ) = ( π , 3) in the mathematician’s polar scheme. It is implied from this that the angle is

(a) negative

(b) expressed in radians

(c) greater than 360°

(d) ambiguous

3. Suppose a point has the coordinates ( θ , r ) = ( π /4,6) in the mathematician’s polar scheme. What are the coordinates ( α , r ) of the point in the navigator’s polar scheme?

(a) They cannot be determined without more information

(b) (–45°, 6)

(c) (45°, 6)

(d) (135°, 6)

4. Suppose we are given the simple relation g ( x ) = x. In Cartesian coordinates, this has the graph y = x. What is the equation that represents the graph of this relation in the mathematician’s polar coordinate system?

(a) r = θ

(b) r = 1/θ, where θ ≠ 0°

(c) θ = 45°, where r can range over the entire set of real numbers

(d) θ = 45°, where r can range over the set of non-negative real numbers

5. Suppose we set off on a bearing of 135° in the navigator’s polar coordinate system. We stay on a straight course. If the starting point is considered the origin, what is the graph of our path in Cartesian coordinates?

(a) y = x, where x ≥ 0

(b) y = 0, where x ≥ 0

(c) x = 0, where y ≥ 0

(d) y = – x , where x ≥ 0

6. The direction angle in the navigator’s polar coordinate system is measured

(a) in a clockwise sense

(b) in a counterclockwise sense

(c) in either sense

(d) only in radians

7. The graph of r = –3θ in the mathematician’s polar coordinate system looks like

(a) a circle

(b) a cardioid

(c) a spiral

(d) nothing; it is undefined

8. A function in polar coordinates

(a) is always a function in rectangular coordinates

(b) is sometimes a function in rectangular coordinates

(c) is never a function in rectangular coordinates

(d) cannot have a graph that is a straight line

9. Suppose we are given a point and told that its Cartesian coordinate is ( x , y ) = (0, –5). In the mathematician’s polar scheme, the coordinates of this point are

(a) ( θ , r ) = (3π/2, 5)

(b) ( θ , r ) = (3π/2, –5)

(c) ( θ , r ) = (–5, 3π/2)

(d) ambiguous; we need more information to specify them

10. Suppose a radar unit shows a target that is 10 kilometers away in a southwesterly direction. It is moving directly away from us. When its distance has doubled to 20 kilometers, what has happened to the x and y coordinates of the target in Cartesian coordinates? Assume we are located at the origin.

(a) They have both doubled

(b) They have both increased by a factor equal to the square root of 2

(c) They have both quadrupled

(d) We need to specify the size of each unit in the Cartesian coordinate system in order to answer this question

Answers:

1. c

2. b

3. c

4. c

5. d

6. a

7. c

8. b

9. a

10. a