of input and output, a parameterization for f ) is (f(t), t).) Activity 9.6.3. Vector-valued functions can be used to generate many Interesting curves. Graph each of the following using an appropriate technological tool, and then write one sentence for each function to describe the behavior of the resulting curve. a. r(t) = (t cos(t), t sin(t)) b. r(t) - (sin(t) cos(t), t sin(t)) C. r(t) - (sin (5t), sin(4t)) d. r(t) - (t sin(t) cos(t), 0.9t cos(t?), sin(t)) (Note that this defines a curve in 3-space.) e. Experiment with different formulas for z (t) and y(t) and ranges for t to see what other interesting curves you can generate. Share your best results with peers. Recall from our earlier work that the traces and level curves of a function are themselves curves in space. Thus, we may determine parameterizations for them. For example, if z - f(r, y) = cos(x2 + y?), they = 1 trace of the function is given by setting y = 1 and letting a be parameterized by the variable t; then, the trace is the curve whose parameterization is (t, 1, cos(t? + 1))