Prerequisite:
Grade of C or higher in MATH 171, or appropriate score on the math assessment test.

Textbook:
Trigonometry, 5^th Edition by C. P. McKeague & M. D. Turner, Thomson Brooks/Cole Publishers

Supplies:
A scientific calculator is required, graphing capabilities are desirable.

Description:

This is a course in trigonometric functions and graphs. Emphasis will be placed on understanding function notation, definitions, algebraic relations, real-world applications, graphing in the real and complex plane, inverse functions, polar functions, and vectors.

Students who take MATH 172 and MATH 173 will receive at most six (6) hours of credit towards graduation.

Course Objectives:
        After completing this course, the student should be able to:

                    1.        Evaluate trigonometric functions.
                    2.        Apply trigonometric functions to real-world situations.
                    3.        Verify trigonometric identities.
                    4.        Solve trigonometric equations.
                    5.        Solve and find areas of triangles using trigonometric formulas.
                    6.        Analyze the graphs of trigonometric, inverse trigonometric, and polar functions.
                    7.        Calculate products, quotients, powers, and roots of complex numbers in trigonometric form.

Content Outline and Competencies:

I.    The Six Trigonometric Functions

• Determine the six trigonometric functions of an angle in standard position given a point on its terminal side.
• Determine the remaining trigonometric functions of an angle given the value of one trigonometric function and the quadrant in which the angle lies.
• Determine the six trigonometric functions of an angle in a triangle given two sides.
• Calculate the six trigonometric functions of an angle using a calculator.
• Determine exact values of the six trigonometric functions given a 30°, 45°, 60°, or quadrantal angle.
• Determine the six trigonometric functions of an angle in standard position using reference angles.

II.    Applications

• Solve real-world problems involving angles of elevation and depression.
• Calculate the length of an arc and the area of a sector in a circle.

III.    Graphs of Trigonometric Functions

• Graph the six basic trigonometric functions of the form y = k + A f (Bx + C).
• Determine the equation of a function given its graph.
• Graph combinations of functions.

IV.    Trigonometric Identities

• Simplify trigonometric expressions using trigonometric identities.
• Prove trigonometric identities.
• Evaluate function values using sum, difference, double, and half angle identities.

V.    Inverse Trigonometric Functions

• Evaluate inverse trigonometric functions with and without a calculator.
• Evaluate expressions involving inverse trigonometric functions.

VI.    Trigonometric Equations

• Solve trigonometric equations on a given interval in degrees or radians.
• Solve trigonometric equations for all angle solutions.

VII.    Triangles

• Solve triangles using trigonometric ratios, the Law of Sines, or the Law of Cosines, where appropriate.
• Find areas of triangles.
• Apply the solutions of triangles to real-world problems.

VIII.    Vectors

• Determine the magnitude and direction of vectors.
• Resolve vectors into components.
• Find the sum, difference, dot product, magnitude, and angle between two vectors in algebraic form.
• Apply vectors to real-world problems.

IX.    Complex Numbers

• Graph in the complex plane.
• Convert complex numbers from standard form to trigonometric form and vice versa.
• Find products, quotients, powers, and roots of complex numbers.

X.    Polar Coordinates

• Convert from rectangular to polar coordinates and vice versa.
• Convert equations from rectangular to polar form and vice versa.
• Graph polar equations.