Question

a.)Find the length of the spiral r=θ for 0 ≤ θ ≤ 2

b.)Find the exact length of the polar curve r=3sin(θ), 0 ≤ θ ≤ π/3

c.)Write each equation in polar coordinates. Express as a function of t. Assume that r>0.

- y=(−9)
r=

- x^2+y^2=8
r=

- x^2 + y^2 − 6x=0

r=

-    x^2(x^2+y^2)=2y^2

r=

Answer 1

(a) L = 2.9579

(b) L =  π

(c) (i) r = -9cosec(t) , -π≤t≤0

(ii) r = 2√2 for all t

(iii) r = 6cost , -π/2 ≤t≤π/2

(iv) r = √2tan(t) , 0≤t<π/2