Plane TrigonometryMTH 121
Prerequisite: Any MTH 119 with a grade of "C" or better or two years of high school algebra. Includes trigonometric functions and their graphs, solution of triangles, identities, trigonometric equations, inverse trigonometric functions, and complex numbers. A GRAPHING CALCULATOR IS REQUIRED.(45-0)
Outcomes and Objectives
Define, identify the characteristics of, and solve problems related to angles.
- 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.)
- Differentiate between radian and degree measure.
- Convert between radian and degree measure.
- Solve problems involving similar triangles.
Student can solve a variety of oblique triangles.
- Use the Law of Sines to solve oblique triangles.
- Use the Law of Cosines to solve oblique triangles.
Student can communicate effectively about mathematics.
Student can use technology appropriately to do mathematics.
- Identify when technology is appropriate for problem solving.
- Evaluate the reasonableness of results.
Student can define and apply the 6 trigonometric ratios.
- Express the relationship between the sides of a right triangle and the 6 trigonometric ratios.
- Evaluate the 6 trigonometric ratios and their inverses with a calculator.
- Use the sign properties of the six trigonometric functions.
- Use reference angles and triangles to determine the values for trigonometric functions whose terminal sides are not in the first quadrant.
- Apply the 6 trigonometric ratios to right triangle problems.
Student can construct and interpret graphs of trigonometric functions.
- Determine the domain and range of a trigonometric function.
- Sketch the graphs of the 6 basic trigonometric functions.
- Graph and interpret transformations of sine and cosine functions.
Student can use and apply inverse trigonometric functions.
- Identify the algebraic and geometric properties of inverse functions.
- Determine the domain and range of the three basic inverse trigonometric functions.
- Sketch the graphs of the 3 basic inverse trigonometric functions.
- Rewrite a composition of trigonometric and inverse trig functions as an algebraic expression.
Student can solve a variety of trigonometric equations.
- Solve trigonometric equations of the form f (x) = a, where f is a basic trigonometric function and a is a real number.
- 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.
- Solve trigonometric equations which are quadratic in form.
Student can use identities to rewrite trigonometric expressions.
- Know and apply Pythagorean identities.
- Know and apply quotient identities.
- Know and apply reciprocal identities.
- Use basic identities (sum, difference, double angle, half angle) to rewrite expressions.
Student can demonstrate an understanding of polar coordinates, polar equations, and polar graphs.
- Plot points in a polar coordinate system.
- Convert between polar and rectangular coordinates.
- Convert equations between polar and rectangular form.
- Graph simple polar equations.
Student can define and use complex numbers in trigonometric form.
- Plot complex numbers in the complex plane.
- Convert complex numbers between rectangle and trigonometric form.
- Apply DeMoivre's Theorem.
- Perform operations with complex numbers in trigonometric form.
Students can demonstrate an understanding of vectors.
- Add and subtract vectors graphically.
- Add and subtract vectors algebraically.
- Use trigonometry to solve problems involving vectors.