The point P shown in the figure has rectangular coordinates
(x, y) =
Correct: Your answer is correct.
.
The same point can be described using polar coordinates. Assuming
r > 0 and 0 ≤ 𝜃 < 2𝜋,
the point P has polar coordinates
(r, 𝜃) =
.
To convert rectangular coordinates to polar coordinates, we can use the formulas:
r = √(x^2 + y^2)
θ = arctan(y / x), where arctan is the inverse tangent function
Given (x, y), we can calculate r and θ as follows:
r = √(x^2 + y^2)
r = √((-4)^2 + (-3)^2)
r = √(16 + 9)
r = √25
r = 5
θ = arctan(-3 / -4)
θ = arctan(0.75)
θ ≈ 0.6435
Therefore, the polar coordinates of point P are (5, 0.6435).