1. Let x = t + cos(t) and y = t – sin(t) for 0≤t≤2π a.

Question

Find the coordinates of the initial point (t = 0) and the end point (t = 2π).?

b. Graph the parametric curve. 
c. Find the length of the curve.

Answer 1

(a).

The equations are x = t + cos(t) and y = t - sin(t).

Substitute t = 0 in the original equations.

x = 0 + cos(0) = 1

y =  0 - sin(0) = 0

The initial point (x, y) = (1, 0).

Substitute t = 2pi in the original equations.

x = 2pi + cos(2pi) = 2pi + 1

y =  2pi - sin(2pi) = 2pi

The end point (x, y) = (2pi + 1, 2pi).