Course goals and learning outcomes support the Foundational Component Areas defined by the Texas Higher Education Coordinating Board. Course goals are linked to the respective Core Curriculum Competencies: Critical Thinking Skills, Communication Skills, and Empirical and Quantitative Skills. Specific competencies are identified in designated course goals and learning outcomes.

Upon successful completion of this course, students will:

Demonstrate and apply knowledge of properties of functions by
1. explaining properties of trigonometric functions;
2. identifying the domain and the range of trigonometric functions;
3. defining the inverse trigonometric functions;
4. applying inverse function notation.
Recognize and apply algebraic and transcendental functions and solve related equations by
1. solving trigonometric equations involving a single function;
2. solving equations using trigonometric identities;
3. solving trigonometric equations with multiple angles.
Apply graphing techniques to algebraic and transcendental functions by
1. graphing basic trigonometric functions;
2. determining amplitude, period, and phase shift;
3. graphing arcsine x, arcos x, and arctan x.
Compute the values of trigonometric functions for key angles in all quadrants of the unit circle measured in both degrees and radians by
1. using the relationship between degree and radian measure;
2. defining trigonometric functions using the unit circle approach;
3. defining right triangle trigonometric functions;
4. determining both exact and approximate value of trigonometric functions.
Prove trigonometric identities by
1. listing the fundamental identities: ratio, reciprocal, Pythagorean, and cofunction;
2. applying the fundamental identities to verify other identities.
Solve right and oblique triangles by
1. solving right triangle problems;
2. using the Law of Sines and the Law of Cosines to solve triangle problems;
3. choosing appropriate techniques to solve any triangle problem.
Use the concepts of trigonometry to solve applications by
1. computing arc length;
2. computing area of circular sectors;
3. computing angular and linear velocity;
4. relating angular velocity to linear velocity;
5. solving applied right triangle problems.
Examine complex numbers by
1. performing operations on complex numbers;
2. converting between rectangular and trigonometric forms of complex numbers;
3. performing multiplication and division of complex numbers in trigonometric form;
4. computing integral powers and nth roots of complex numbers.
Examine topics from analytical geometry by
Demonstrate knowledge of sequence and series by
1. distinguishing between a sequence and a series;
2. using the basic formulas for an arithmetic sequence and a geometric sequence;
3. using summation formulas for series notation;
4. determining the sum of an arithmetic series, a finite geometric series, and an infinite geometric series if possible;
5. applying the binomial theorem.
Demonstrate lab skills by
1. investigating the properties of angles;
2. analyzing trigonometric functions on the unit circle and on a right triangle;
3. using trigonometric functions to construct graphs, solve equations, and verify identities;
4. analyzing triangles to determine unknown parts;
5. relating rectangular coordinates to polar coordinates;
6. investigating complex numbers and their properties;
7. examining sequences and series;
8. analyzing the equations of conic sections.
Critical Thinking Skills: Demonstrate the ability to evaluate, synthesize, and perform inquiry and analysis of information in mathematical problems by
1. distinguishing between the different types of functions;
2. identifying characteristics of trigonometric functions.
Communication Skills: Demonstrate the ability to communicate orally, visually, and/or in writing using mathematical language and symbols by
1. analyzing and interpreting graphs;
2. illustrating the solution steps to solve trigonometric equations.
Empirical and Quantitative Skills: Manipulate and analyze numerical data or observable facts in making informed conclusions by
1. performing operations with sequences and/or series;
2. solving trigonometric equations;
3. solving applications of conic sections.

MATH 2412

Download as PDF

MATH 2412 - Pre-Calculus Math