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# MAT 130 - Trigonometry

Course Department: Mathematics
Last Date of Approval: Fall 2018

3 Credits
Total Lecture Hours: 45
Total Lab Hours: 0
Total Clinical Hours: 0
Total Work-Based Experience Hours: 0

Course Description:
This course contains an orderly development of the trigonometric functions and their inverses. Topics included in the course are identities, trigonometric equations, graphs, and solutions of triangles. This course will also help students gain mathematical literacy which will be of vital significance when making important life decisions. In addition, this course will help with any career that involves mathematics, decision making, or problem-solving. This course satisfies a general education requirement in the Math/Science area.

Prerequisites: MAT 102 - Intermediate Algebra  with C grade or better or the necessary score on the mandatory assessment and placement chart found in the course catalog.

Credit for Prior Learning: There are no Credit for Prior Learning opportunities for this course.

Course Fees: ebook/Access Code: \$90.00

Common Course Assessment(s): None

Student Learning Outcomes and Objectives:
Student Learning Outcomes:

1. Outcome 1: Analyze and use trigonometric functions.
2. Outcome 2: Construct graphs of trigonometric functions.
3. Outcome 3: Investigate trigonometric identities.
4. Outcome 4: Solve trigonometric equations.

Unit Objectives:

Outcome 1: Analyze and use trigonometric functions.

Task 1: Find the unknown quantity in the formula s = rθ where θ is in either degree or radian units.

Task 2: State the definitions of the trig functions in terms of x, y and r.

Task 3: State the definitions of the trig functions in a right triangle.

Task 4: Find the values of any trig function of an angle given a point on its terminal side.

Task 5: Find the value of any trig function given the value of any other trig function.

Task 6: State the values of the six trig functions of the special angles 0°, 30°, 45°, 60°, 90°, 120°, etc. without using a calculator.

Task 7: Use a calculator to find the approximate value of the trig function of any angle.

Task 8: Use a calculator to find the angle in a specified quadrant that has a given trig function value.

Task 9: State the sign (+ or -) of the trig function in any of the four quadrants.

Task 10: Find the reference angle for a given angle.

Task 11: Solve a right triangle given either two sides or one side and one angle.

Task 12: Find an unknown distance or angle for an application that involves a single right triangle.

Task 13: Find an unknown distance or angle for an application that involves more than one right triangle.

Task 14: Find an unknown part of an oblique triangle with the Law of Sines.

Task 15: Find an unknown part of an oblique triangle with the Law of Cosines.

Task 16: Find all of the unknown parts of an oblique triangle for the four cases of SAS, SSS, AAS and SSA.

Task 17: Determine the number of solutions that are possible for the ambiguous case (SSA).

Task 18: Find the area of an oblique triangle using an appropriate formula.

Task 19: Convert the degree measure of an angle to radian measure in either pi or decimal form.

Task 20: Convert the pi or decimal form of the radian measure of an angle to degree measure.

Task 21: State the exact values of trig functions of special angles when radian measure is used without using a calculator.

Task 22: Use a calculator to find the approximate value of the trig function of any angle.

Task 23: Find the area of a sector of a circle where the central angle is in either degree or radian units.

Task 24: Perform operations on the algebraic form of complex numbers.

Task 25: Convert the algebraic form of a complex number to trigonometric form.

Task 26: Convert the trigonometric form of a complex number to algebraic form.

Task 27: Find products and quotients of complex numbers using trigonometric form.

Task 28: Find powers and roots of complex numbers using trigonometric forms.

Task 29: Convert a polar equation to Cartesian form.

Task 30: Convert a Cartesian equation to polar form.

Outcome 2: Construct the graph of trigonometric functions.

Task 1: Find the amplitude of the graph of a given trig function.

Task 2: Find the period of the graph of a given trig function.

Task 3: Find the vertical translation of the graph of a given trig function.

Task 4: Find the phase shift of the graph of a given trig function.

Task 5: Draw the graph of any function that contains a single trig function.

Task 6: Plot points using polar coordinates.

Task 7: Draw graphs of polar equations.

Outcome 3: Investigate trigonometric Identities.

Task 1: Find the exact values of trig functions of special angles using sum and difference identities.

Task 2: Find the exact values of trig functions of special angles using double-angle and half-angle identities.

Task 3: Given trig function values of two angles, find the trig function values of their sum and difference.

Task 4: Given trig function values of an angle, find the trig function values of an angle that is twice or half as large.

Task 5: Simplify or evaluate trig expressions involving negative angles.

Task 6: Verify trig identities using the eight fundamental identities.

Task 7: Verify trig identities using the sum and difference, double-angle and half-angle identities.

Task 8: Rewrite a given trig function as a cofunction of a complementary angle.

Outcome 4: Solve trigonometric equations.

Task 1: Find the values of expressions containing inverse trig functions of special values without using a calculator.

Task 2: Use a calculator to find the values of expressions containing inverse trig functions of any values.

Task 3: Solve trig equations containing functions whose variables have coefficients of 1.

Task 4: Solve trig equations containing functions of half-angles and multiples of angles.

Task 5: Solve equations that contain inverse trig functions.

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