A curve is described by the parametric equations
x=5cost,y=4sint−sin2t,
with 0≤t≤2π.
a. (i) Find all values of t in the stated interval for which the tangent to the curve is horizontal.
b. (ii) Write the coordinates of every point on the curve where a horizontal tangent occurs.
c. (iii) How many distinct horizontal tangents does the curve possess in the interval 0≤t≤2π? Give reasons for your answer.