# 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 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.