Find the smallest value?

Question

Find the smallest value of θ in the interval [0, 2pi] for which the rose r=2 cos (5θ) passes through the origin.

 

Answer: pi/10

 

Show your work.

Answer 1

The zeroes of cos(x) are at the odd multiples of π/2.  We need to have 5θ=(2k+1)π/2 or that θ=(2k+1)π/10, for k some integer.  The smallest value of θ = π/10.