The so-called logarithmic spiral was first studied in the late 17th century by t

Question

The so-called logarithmic spiral was first studied in the late 17th century by the Swiss mathematician Jacob Bernoulli. He liked this spiral so much that he had it carved on his tomb stone---just as Archimedes was supposed to have done with the Archimedean spiral. The logarithmic spiral is given by the vector equation r(t)=<et cos(t),et sin(t)> .

a) Show that the angle between the position vector r(t) and the tangent vector r'(t) is constant.

b) Find the arc length of the curve from t=0 to t=a .

****Please show all work!!!!

Explanation / Answer

Solution:

a) r(t)=(etcost, etsint) The position vector

r'(t)=(etcost-etsint, etsint+etcost)

The angle is

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