Question

Which rectangular equation is equivalent to the polar equation rcos θ = -2?

A) x = -2
B) x = -2cos(θ)
C) x = 2cos(θ)
D) x = -2cos(θ)^2

Answer 1

The rectangular equation equivalent to the polar equation rcos θ = -2 is x = 2cos(θ).

Step-by-step explanation:

The rectangular equation that is equivalent to the polar equation rcos θ = -2 is Option C) x = 2cos(θ).

In the polar coordinate system, the equation rcos θ = -2 represents a line in the rectangular coordinate system where x is equal to 2cos(θ). This means that the x-coordinate is equal to 2 times the cosine of the angle θ.

For example, if θ = 45°, then x = 2cos(45°) = 2(√2/2) = √2. So the point on the line in the rectangular coordinate system would be (√2, y).