Point (5, 5/3) has polar coordinates (2√10/3, 19.1°) and (2√10/3, 199.1°) due to angle ambiguity. So the correct option is B.
The question asks you to:
1. Plot the point with rectangular coordinates (5, 5/3).
2. Give two pairs of polar coordinates for the point, where 0° < θ < 360°.
To convert rectangular coordinates to polar coordinates, you can use the following formulas:
* r = √(x² + y²)
* θ = tan^-1(y/x)
For the point (5, 5/3), you would get:
* r = √(5² + (5/3)²) = √(40/9) = 2√10/3
* θ = tan^-1((5/3) / 5) = tan^-1(1/3)
There are two solutions for θ in the range 0° < θ < 360°:
* θ1 = 19.1°
* θ2 = 199.1°
Therefore, two possible pairs of polar coordinates for the point (5, 5/3) are:
* (2√10/3, 19.1°)
* (2√10/3, 199.1°)
The plot of the point and the two possible polar coordinates is shown in the image you sent.
The correct answer is (b) (2√10/3, 19.1°), (2√10/3, 199.1°).