Show that the curve with parametric equations ,

MATHEMATICS · Subjective · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

Show that the curve with parametric equations

x = \sin t

y = \cos t

z = \sin^2 t

is the curve of intersection of the surfaces

z = x^2

and

x^2 + y^2 = 1

. Use this fact to help sketch the curve.