How do I write a relationship between x and y from these par

How do I write a relationship between x and y from these parametrics?

After graphing the parametrics x=cos(t) and y=sin(t) on a calculator, notice the starting point and the direction of the motion. Notice what the graph looks like. Now eliminate \"t\" and write an equation for the relation between x and y?

Solution

From the parametric equations: x = cos t and y = sin t, a relation can be created by first expressing t as a function of x.

As cos x = t

=> t = arc cos (x)

Substitute this expression for t in y = sin t

y = sin (arc cos (x))

The relationship between y and x is given by y = sin (arc cos (x)).