MTH 121 - Plane Trigonometry

1.  Solve problems related to angles.
   1. Define basic terminology of angles and triangles (initial side, terminal side, vertex, positive angle, negative angle, coterminal angles, right angle, straight angle, acute angle, obtuse angle, complementary angles, supplementary angles.)
   2. Identify the characteristics of angles and triangles.
   3. Differentiate between radian and degree measure.
   4. Convert between radian and degree measure.
   5. Solve problems involving similar triangles.
2. Apply the six trigonometric ratios.
   1. Define the six trigonometric ratios.
   2. Express the relationship between the sides of a right triangle and the six trigonometric ratios.
   3. Evaluate the six trigonometric ratios and their inverses with a calculator.
   4. Use the sign properties of the six trigonometric functions.
   5. Use reference angles and triangles to determine the values for trigonometric functions whose terminal sides are not in the first quadrant.
   6. Apply the six trigonometric ratios to right triangle problems.
3. Demonstrate an understanding of the graphs of trigonometric functions.
   1. Determine the domain and range of a trigonometric function.
   2. Sketch the graphs of the six basic trigonometric functions.
   3. Graph and interpret transformations of sine and cosine functions.
4. Demonstrate an understanding of the inverse trigonometric functions.
   1. Identify the algebraic and geometric properties of inverse functions.
   2. Determine the domain and range of the three basic inverse trigonometric functions.
   3. Sketch the graphs of the three basic inverse trigonometric functions.
   4. Rewrite a composition of trigonometric and inverse trigonometric functions as an algebraic expression.
   5. Apply inverse trigonometric functions in problem solving.
5. Solve a variety of trigonometric equations.
   1. Solve trigonometric equations of the form f (x) = a, where f is a basic trigonometric function and a is a real number.
   2. Solve trigonometric equations of the form f (kx) = a, where f is a basic trigonometric function, k is a natural number, and a is a real number.
   3. Solve trigonometric equations which are quadratic in form.
6. Use identities to rewrite trigonometric expressions.
   1. Apply Pythagorean identities.
   2. Apply quotient identities.
   3. Apply reciprocal identities.
   4. Use basic identities (sum, difference, double angle, half angle) to rewrite expressions.
7. Demonstrate an understanding of the polar graphing system.
   1. Plot points in a polar coordinate system.
   2. Convert between polar and rectangular coordinates.
   3. Convert equations between polar and rectangular form.
   4. Graph simple polar equations.
   5. Identify symmetries in polar graphs.
8. Demonstrate an understanding of complex numbers in trigonometric form.
   1. Define complex numbers in the trigonometric form.
   2. Plot complex numbers in the complex plane.
   3. Convert complex numbers between rectangular and trigonometric form.
   4. Perform operations with complex numbers in trigonometric form.
9.  Demonstrate an understanding of vectors.
   1. Add and subtract vectors graphically.
   2. Add and subtract vectors algebraically.
   3. Solve problems involving vectors.
10. Solve a variety of oblique triangles.
    1. Use the Law of Sines to solve oblique triangles.
    2. Use the Law of Cosines to solve oblique triangles.
11. Demonstrate an understanding of parametric equations.
    1. Sketch graphs of parametric equations.
    2. Convert between parametric and rectangular equations.
    3. Solve problems with parametric equations.
12. Communicate effectively about mathematics.
13. Use technology appropriately to do mathematics.