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
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
(b) expressed in radians
(c) greater than 360°
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
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