Find the polar coordinates of a vector in standard notation that has polar coordinates of (4, 30°). Round to tenths.
A)(0.6, -4.0)
B)(3.5, 2)
C)(0.6, 2)
D)(3.5, 30°)

Question

Quizplus · Accepted Answer

To convert from polar coordinates (r, θ) to rectangular coordinates (x, y), we use the formulas x = r cos θ and y = r sin θ. Therefore, for the given polar coordinates of (4, 30°), we have x = 4 cos(30°) = 3.5 and y = 4 sin(30°) = 2.0. Thus, the rectangular coordinates are (3.5, 2.0). To convert back to polar coordinates, we use the formulas r = √(x^2 + y^2) and θ = atan2(y, x) (where atan2 is the two-argument arctangent function that takes sign into account to determine the quadrant of the result). Therefore, we have r = √(3.5^2 + 2.0^2) = 4.1 and θ = atan2(2.0, 3.5) = 30.4° (rounded to tenths). Thus, the polar coordinates in standard notation are (4.1, 30.4°), which is closest to choice B of (3.5, 2).

Find the Polar Coordinates of a Vector in Standard Notation