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Plane Trigonometry

MTH 121

Plane Trigonometry

MTH 121

Course Description

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.

Objectives:

  • 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.

Objectives:

  • 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.

Objectives:

  • Identify when technology is appropriate for problem solving.
  • Evaluate the reasonableness of results.

Student can define and apply the 6 trigonometric ratios.

Objectives:

  • 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.

Objectives:

  • 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.

Objectives:

  • 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.

Objectives:

  • 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.

Objectives:

  • 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.

Objectives:

  • 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.

Objectives:

  • 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.

Objectives:

  • Add and subtract vectors graphically.
  • Add and subtract vectors algebraically.
  • Use trigonometry to solve problems involving vectors.