For , the motion of a point in the plane is given by and…
MATHEMATICS · Multi-part · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices
Problem
For 0≤t≤2π, the motion of a point in the plane is given by x=sin2t and y=sint.
(i) Compute all values of t in the given interval for which the tangent to the curve is horizontal.
(ii) Compute all values of t in the given interval for which the tangent to the curve is vertical.
(iii) Write the coordinates of each point corresponding to parts (i) and (ii).
(iv) Prove that there is no point on the curve within 0≤t≤2π at which the tangent is simultaneously horizontal and vertical.