Course Number and Title: ACM 023 Trigonometry & Pre-Calculus B
This course integrates intermediate algebra, analytic geometry, and trigonometry with other college algebra topics through a functional approach as preparation for calculus.
Access to a computer and the Internet TI-83 Graphing Calculator
- Solve linear and nonlinear systems. (CCC 2, 6)
- Perform operations on matrices. (CCC 2, 6)
- Solve trigonometric application problems using oblique triangle principles. (CCC 2, 6)
- Define complex numbers in trigonometric form. (CCC 1)
- Solve problems of applications involving vectors. (CCC 2, 6)
- Demonstrate principles of analytic geometry working with conic sections. (CCC 2, 6)
- Define parametric equations and polar coordinates, and investigate their graphs. (CCC 2, 6)
- Solve problems involving infinite sequences and series. (CCC 2, 6)
See Core Curriculum Competencies and Program Graduate Competencies at the end of the syllabus. CCPOs are linked to every competency they develop.
Upon completion of this course, the student will:
- Solve linear and nonlinear systems.
- Solve linear system of equations by graphing, substitution, elimination, matrices, and Cramer’s rule.
- Solve a system of linear inequalities.
- Solve application problems using linear programming.
- Decompose rational expressions into partial fractions.
- Solve and graph nonlinear system of equations.
- Perform operations on matrices.
- Add, subtract, and multiply matrices.
- Find the inverse of a matrix.
- Solve trigonometric application problems using oblique triangle principles.
- Apply trigonometric functions to right triangles.
- Solve oblique triangles using the law of sines or law of cosines.
- Define complex numbers in trigonometric form.
- Graph complex numbers.
- Convert complex numbers from rectangular form to trigonometric form and vice versa.
- Add, subtract, multiply, and divide complex numbers in trigonometric form.
- Solve problems of applications involving vectors.
- Find the resultant of vectors.
- Perform calculations on vectors in component form.
- Solve applied problems involving vectors.
- Demonstrate principles of analytic geometry working with conic sections.
- Given an equation of a parabola, find the vertex, the focus, and the directrix.
- Given an equation of a circle, find the center and the radius.
- Given the equation of an ellipse, find the center, the vertices, and the foci.
- Given the equation of a hyperbola, find the center, the vertices, and the foci.
- Graph each of the conic sections.
- Write the equation for each of the conic sections given the appropriate data.
- Define parametric equations and polar coordinates, and investigate their graphs.
- Graph parametric and polar equations.
- Convert equations form rectangular form to polar form and vice versa.
- Determine an equivalent rectangular equation for parametric equations and vice versa.
- Determine the location of a moving object at a specific time.
- Solve problems involving infinite sequences and series.
- Look for a pattern in a sequence, and determine a general term.
- Construct the terms of recursively defined sequence.
- For an arithmetic or geometric sequence, find the nth term.
- Find the common difference, and construct the arithmetic sequence.
- Find the common ratio, and construct the geometric sequence.
- Find the sum of an arithmetic or infinite geometric sequence.
Students will demonstrate proficiency on all Core Course Performance Objectives at least to the 75 percent level to successfully complete the course. The grade will be determined using the Academic Challenge Grading System:
Students should refer to the Student Handbook for information on the Academic Standing Policy, the Academic Integrity Policy, Student Rights and Responsibilities, and other policies relevant to their academic progress.
- Apply clear and effective communication skills.
- Use critical thinking to solve problems.
- Collaborate to achieve a common goal.
- Demonstrate professional and ethical conduct.
- Use information literacy for effective vocational and/or academic research.
- Apply quantitative reasoning and/or scientific inquiry to solve practical problems.
The College is committed to providing reasonable accommodations for students with disabilities. Students are encouraged to schedule an appointment with the campus Disabilities Support Counselor to request an accommodation needed due to a disability. A listing of campus Disabilities Support Counselors and contact information can be found at the disabilities services web page or visit the campus Advising Center.