Final answer:
To plot the point represented by the polar coordinates (-9, -π/6), we need to find the Cartesian coordinates by using the formulas x = r * cos(θ) and y = r * sin(θ). The Cartesian coordinates of the point are (-4.5, -4.5).
Step-by-step explanation:
To plot the point represented by the polar coordinates (-9, -π/6), we first need to understand that the first number (-9) represents the distance from the origin (the radial coordinate) and the second number (-π/6) represents the angle the radial vector makes with the positive x-axis (the angular coordinate).
In this case, the distance from the origin is 9 units and the angle is -π/6 (which is in the third quadrant). To find the Cartesian coordinates, we can use the following formulas:
x = r * cos(θ)
y = r * sin(θ)
Substituting the values, we get:
x = 9 * cos(-π/6) = 9 * (√3/2) = -4.5 units
y = 9 * sin(-π/6) = 9 * (-1/2) = -4.5 units
So, the Cartesian coordinates of the point are (-4.5, -4.5).