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goldenfox [79]
3 years ago
9

Find the exact length of the curve. Use a graph to determine the parameter interval.. r = (cos(θ/2))^2

Mathematics
1 answer:
harkovskaia [24]3 years ago
8 0
Cos(2θ) = 2cos^2θ - 1, 

<span> cos^2(θ/2) </span>
<span>Solving  </span>
<span>cos^2θ = [1 + cos(2θ)]/2. </span>

<span>replacing θ with θ/2 gives. </span>
<span>cos^2(θ/2) = (1 + cosθ)/2. </span>

<span>length of a polar curve of the form r = f(θ) on [a, b] is given by: </span>
<span>L = ∫ √[r^2 + (dr/dθ)^2] dθ (from θ=a to b). 
hope this helps</span>
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