When eliminating the parameter I know how to get rid of the

When eliminating the parameter, I know how to get rid of the t when there is one, but what do I do if there isnt a t for instance x=sintheta, y=costheta, 0<equal theta<equal pi....How do I detemine the t or does there even need to be a t? Please clarify my thoughts. Thank You

here you have to use identity sin^2 @ + cos^2 @ = 1 this is only way to remove parameter in it