Answer:
3. (3, -90°)
4. (√3, 150°)
Step-by-step explanation:
You want the polar coordinates corresponding to the rectangular coordinates (0, -3) and (-3/2, √3/2).
Polar coordinates
The polar coordinates can be found as ...
(x, y) ⇔ r∠θ
where ...
r = √(x² +y²)
θ = arctan(y/x) . . . . . . with attention to quadrant
3. (0, -3)
With the calculator in degrees mode, we have ...
r = √(0² +(-3)²) = √9 = 3
θ = arctan(-3/0) = -90° . . . . . . a point on the -y axis
(0, -3) ⇔ (3, -90°)
4. (-3/2, √3/2)
r = √((-3/2)² +(√3/2)²) = √(9/4 +3/4) = √3
θ = arctan((√3/2)/(-3/2)) = arctan(-1/√3) = 150° . . . . in the 2nd quadrant
(-3/2, √3/2) ⇔ (√3, 150°)
__
Additional comment
A suitable scientific or graphing calculator can do these conversions for you. Different calculators use different formats for the coordinates. The one shown in the attachment keeps these as complex numbers.
A different calculator may keep them as a vector, [√3 5π/6], for example. In this latter case, the user is expected to keep track of the meanings of the vector components, as rectangular vectors look just like polar vectors.
