The Humongous Book of Trigonometry Problems

Parametric Equations

Two equations that describe one curve

Note: Problems 17.1–17.4 refer to the curve defined by parametric equations x = t + 3 and y = 2t – 1.

17.1    Identify the point on the curve that corresponds with t = –3.

A parametrically defined graph uses individual equations to represent the coordinates of each point. In this problem, the x- and y-coordinates of each point are defined in terms of a third variable t called the parameter. Substitute t = –3 into both of the parametric equations to identify the coordinates of one point on the graph of the parametric curve.

Thus, the parameter t = –3 corresponds with the rectangular coordinates ...