In Exercises use the result of Exercise 54 to approximate the distance between the two points in polar coordinates.

Data from in Exercise 54

(a) Verify that the Distance Formula for the distance between the two points (r₁, θ₁) and (r₂, θ₂) in polar coordinates is

(b) Describe the positions of the points relative to each other for θ₁ = θ₂. Simplify the Distance Formula for this case. Is the simplification what you expected? Explain.

(c) Simplify the Distance Formula for θ₁ - θ₂ = 90°. Is the simplification what you expected? Explain.

(d) Choose two points on the polar coordinate system and find the distance between them. Then choose different polar representations of the same two points and apply the Distance Formula again. Discuss the result.

Transcribed Image Text:

d = √√√r² + r²- 2r₁ r₂ cos(0₁ - 0₂).