MTH 121 - Plane Trigonometry

1. Define, identify the characteristics of, and 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. Differentiate between radian and degree measure.
   3. Convert between radian and degree measure.
   4. Solve problems involving similar triangles.
2. Student can define and apply the 6 trigonometric ratios.
   1. Express the relationship between the sides of a right triangle and the 6 trigonometric ratios.
   2. Evaluate the 6 trigonometric ratios and their inverses with a calculator.
   3. Use the sign properties of the six trigonometric functions.
   4. Use reference angles and triangles to determine the values for trigonometric functions whose terminal sides are not in the first quadrant.
   5. Apply the 6 trigonometric ratios to right triangle problems.
3. Student can construct and interpret graphs of trigonometric functions.
   1. Determine the domain and range of a trigonometric function.
   2. Sketch the graphs of the 6 basic trigonometric functions.
   3. Graph and interpret transformations of sine and cosine functions.
4. Student can use and apply 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 3 basic inverse trigonometric functions.
   4. Rewrite a composition of trigonometric and inverse trig functions as an algebraic expression.
5. Student can 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. Student can use identities to rewrite trigonometric expressions.
   1. Know and apply Pythagorean identities.
   2. Know and apply quotient identities.
   3. Know and apply reciprocal identities.
   4. Use basic identities (sum, difference, double angle, half angle) to rewrite expressions.
7. Student can demonstrate an understanding of polar coordinates, polar equations, and polar graphs.
   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.
8. Student can define and use complex numbers in trigonometric form.
   1. Plot complex numbers in the complex plane.
   2. Convert complex numbers between rectangle and trigonometric form.
   3. Apply DeMoivre's Theorem.
   4. Perform operations with complex numbers in trigonometric form.
9. Students can demonstrate an understanding of vectors.
   1. Add and subtract vectors graphically.
   2. Add and subtract vectors algebraically.
   3. Use trigonometry to solve problems involving vectors.
10. Student can 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. Student can communicate effectively about mathematics.
12. Student can use technology appropriately to do mathematics.
    1. Identify when technology is appropriate for problem solving.
    2. Evaluate the reasonableness of results.