Parametric to polar equations Find an equation of the following curve in polar coordinates and describe the curve. x = (1 + cos t) cos t, y = (1 + cos t) sin t, 0 leq t leq 2pi

Mylo O'Moore 2021-01-08 Answered
Parametric to polar equations Find an equation of the following curve in polar coordinates and describe the curve. x=(1+cost)cost,y=(1+cost)sint,0t2π
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tabuordg
Answered 2021-01-09 Author has 99 answers

Step 1

Consider the given curves, x=(1+cost)cost
y=(1+cost)sint Square and add the above equations, x2+y2=(1+cost)2 Divide the above equations, xy=(1+cost)sint(1+cost)cost=tant

Step 2

x2+y2=(1+cost)2
(1+cost)2=1+(1sect)2
(1+1sect)2=(1+1(1+tant2))2 Therefore, x2+y2=(1+1(1+tant2))2
=(1+1(1+11+(xy)2))2)
=(1+1((x2+y2x2)))2
=(1+x(x2+y2))2

Step 3

For polar form, substitute x=rcosθ,y=rsinθ,r2=x2+y2,θ=tan(1)(yx)
x2+y2(1+x((x2+y2)))2
r2=(+(rcosθsqrt(r2))2
r2=(1+cosθ)2 Thus, the required solution is r=1+cosθ

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Jeffrey Jordon
Answered 2021-10-14 Author has 2313 answers

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