1) When completely analyzing G(t) = 2 sin (t - /3) - 1 with its natural domain, we would identify

the critical numbers. They would identify where the maximums and minimums occur. We now have two approaches to finding the critical numbers. They should give the same results.

a) In the first method, we understand the template sin (inside). We know what the inside must equal for the critical numbers. Use your knowledge of sin(inside) to locate all of the critical numbers of G(t).

b) The second method uses derivatives. We can now get the derivative of 2 sin (t - /3)- 1 and then the critical numbers of G(t) are the zeros of the derivative. Identify the zeros of the derivative as critical numbers.

c) Did they give the same results?

2)The Cartesian point (a, b) is also described by the polar coordinates (r, t). a)

What are the Cartesian coordinates of the point described by the polar coordinates (r, - t).

b) What are the Cartesian coordinates of the point described by the polar coordinates (r, -t).

c) What are the Cartesian coordinates of the point described by the polar coordinates (r, + t).

d) What are the Cartesian coordinates of the point described by the polar coordinates (r, 2+ t).