Find r'(t), r(t₀), and r'(t₀) for the given value of t₀. Then sketch the plane curve represented by the vector-valued function, and sketch the vectors r(t₀) and r'(t₀). Position the vectors such that the initial point of r(t₀) is at the origin and the initial point of r'(t₀) is at the terminal point of r(t₀). What is the relationship between r'(t₀) and the curve?

 

r(t) = 3 sin ti + 4 cos tj, to || TT 2