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Use the Distance Formula d = r12 + r22 − 2r1r2 cos(𝜃1 − 𝜃2) to find the distance between the two points in polar coordinates. (Round your answer to one decimal place.) 5, 5𝜋6,    7, 𝜋3

Question

Use the Distance Formula d = r12 + r22 − 2r1r2 cos(𝜃1 − 𝜃2) to find the distance between the two points in polar coordinates. (Round your answer to one decimal place.) 5, 5𝜋6,    7, 𝜋3

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Solution

Sure, let's use the distance formula for polar coordinates to find the distance between the two points. The formula is d = sqrt(r1^2 + r2^2 - 2r1r2*cos(θ1 - θ2)).

Here, r1 = 5, r2 = 7, θ1 = 5π/6, and θ2 = π/3.

Step 1: Calculate θ1 - θ2 θ1 - θ2 = 5π/6 - π/3 = π/2

Step 2: Calculate cos(θ1 - θ2) cos(π/2) = 0

Step 3: Substitute r1, r2, and cos(θ1 - θ2) into the formula d = sqrt((5^2) + (7^2) - 257*0) d = sqrt(25 + 49) d = sqrt(74)

So, the distance between the two points in polar coordinates is approximately 8.6 (rounded to one decimal place).

This problem has been solved

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