Final answer:
To match the given polar coordinates (2, 13pi/6) with points a, b, c, or d, we first standardize the angle by subtracting multiples of 2pi, obtaining the equivalent coordinates (2, pi/6). We can then convert these to Cartesian coordinates, if needed, using x = 2 * cos(pi/6) and y = 2 * sin(pi/6).
Step-by-step explanation:
The student is asking about converting a point given in polar coordinates to match it with a set of points labeled a, b, c, or d. Polar coordinates represent a point in terms of a radius and an angle relative to the origin and the positive x-axis, respectively. The point given is (2, 13pi/6). To convert this to its equivalent in a standard form, we take into account that full rotation in polar coordinates is 2pi radians. Therefore, 13pi/6 is equivalent to pi/6 plus a full rotation (2pi), as 13pi/6 = 2pi + pi/6. The radius is 2, which remains the same after adjusting the angle to the range between 0 and 2pi. Thus, the equivalent polar coordinates are (2, pi/6).
If we were to convert this to Cartesian coordinates, we'd use the formulas x = r * cos(θ) and y = r * sin(θ), where r is the radius and θ is the angle. The Cartesian coordinates would thus be x = 2 * cos(pi/6) and y = 2 * sin(pi/6), which simplifies to x = √3 and y = 1.