Final answer:
To convert the polar coordinates (-7, -π/6) to Cartesian coordinates, use the equations x = r × cos(θ) and y = r × sin(θ). The Cartesian coordinates are approximately (-6.062, 3.5).
Step-by-step explanation:
To convert the polar coordinates (-7, -π/6) to Cartesian coordinates, we recall that polar coordinates are given by (r, θ) where r is the radius (distance from the origin) and θ is the angle in radians. Cartesian coordinates (x, y) can be found using the following equations:
x = r × cos(θ)
y = r × sin(θ)
Plugging in the values given:
x = -7 × cos(-π/6) = -7 × (√3/2)
y = -7 × sin(-π/6) = -7 × (-1/2)
After calculation, the Cartesian coordinates are:
x = -7√3/2
y = 7/2
Therefore, the Cartesian coordinates corresponding to (-7, -π/6) are approximately (-6.062, 3.5).