Show all your work in the space provided under each question. Please write neatly and present your answers in an organized way. There are 150 points possible on this exam; the point value of each problem is indicated: find without using a calculator. Indicate with diagrams how you found your answer. Each part is worth 4 points. (a) (4 pts) sin (b) (4 pts) cos 2 . 4(cid:1: (12 pts) verify the identity tan . 3. (a) (6 pts) find the equation of the ellipse with foci at ( 2, 1) and (6, 1) and major axis of length 10. (b) (6 pts) graph the ellipse in part (a). Indicate the foci, vertices and center on your graph. Page 4 (b) (6 pts) change the rectangular coordinates to polar coordinates: ( 3 3, 3) : in (a) and (b), give an exact answer (not a decimal approximation). For (c), give your answer as an algebraic expression involving x .
