Final answer:
The rectangular coordinates for polar coordinates (2,-60 degrees) are (1, -1.732), which is closest to option C, (1, -1.7). The conversion involves using sine and cosine for the polar to rectangular coordinate transformation.
Step-by-step explanation:
The question is asking to convert polar coordinates to rectangular coordinates. To convert the given polar coordinates (2,-60 degrees) to rectangular coordinates (x, y), we use the formulas x = r cos(\u03b8) and y = r sin(\u03b8), where r is the radius and \u03b8 is the angle in radians.
In this case, r = 2 and \u03b8 = -60 degrees. First, we convert -60 degrees to radians by multiplying by \u03c0/180. So, -60 degrees is equivalent to -\u03c0/3 radians.
Now using the formulas:
- x = 2 cos(-\u03c0/3) = 2 \u00d7 0.5 = 1
- y = 2 sin(-\u03c0/3) = 2 \u00d7 (-\u221a3/2) = -\u221a3 ≈ -1.732
Therefore, the rectangular coordinates for (2,-60 degrees) are approximately (1, -1.732). This is most closely matched by option C, which is (1, -1.7).