Final answer:
The two valid polar coordinates for the point P = (3, -pi/4) are A) (3, -45°) and C) (3, 315°). Options B) and D) do not correctly represent the transformation of the angle -pi/4.
Step-by-step explanation:
To find all polar coordinates of point P where P = (3, -pi/4), we must recognize that polar coordinates consist of a radius and an angle. Given the coordinates (3, -pi/4), we can interpret this as a radius of 3 units and an angle of -pi/4 radians, which is equivalent to -45 degrees. The polar coordinates can be stated in multiple forms, one with a positive radius and a positive angle, and another with a negative radius and the angle increased by 180 degrees to make the point fall into the correct quadrant.
The correct answers from the options given are:
- A) (3, -45°)
- C) (3, 315°), which is the same as -45 degrees but expressed as a positive angle, having added 360 degrees.
Note that while option B) has a radius of -3, this would imply an angle of 135 degrees, not -pi/4 radians. Similarly, option D) has the angle in agreement with the original coordinates but the radius is negative, which is not a valid transformation for the point we are examining.