| By the end of this course, the student will be able to: |
| 1. Prove geometric theorems using the following: |
| · deductive reasoning |
| · analytic techniques with rectangular coordinates |
| 2. Solve for the sides of a triangle using the following: |
| · the Pythagorean Theorem |
| · similar triangles |
| · trigonometric ratios |
| 3. State or identify (from memory) the basic definitions and theorems for the following: |
| · congruent triangles and similar triangles |
| · quadrilaterals |
| · parallel lines, transversals, and associated angles |
| · circles, chords, secants, tangents |
| 4. Write (from memory) the following: |
| · the eight fundamental identities |
| · the double angle identities |
| · the half-angle identities |
| · the sum and difference of angles identities |
| 5. Prove trigonometric identities algebraically |
| 6. Sketch the graphs of trigonometric functions using the following: |
| · amplitude |
| · period |
| · phase shift |
| · vertical translation |
| · reflection |
| 7. Apply inverse trigonometric functions (including their domains
and ranges) in evaluating expressions |
| 8. Solve trigonometric equations |
| 9. Perform mathematical operations with vectors |
| 10. Solve applications involving the following: |
| · congruent/similar triangles |
| · right triangles |
| · law of sines |
| · law of cosines |
| · vectors |
| · arc length and sector area |
| 11. Find products, quotients, powers, and roots of complex numbers
in both rectangular and trigonometric form |