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
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).
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