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# MATH& 142 - Precalculus II

5 Credits

Prepares students for calculus sequence. Concepts, properties and algebra of trigonometric functions, including their graphs, inverses, laws of sines and cosines, identities and equations. Also covers vectors, polar coordinates and conic sections.

Pre-requisite(s) MATH& 141 min 2.0

Placement Eligibility Math 142
Course Note Graphing Calculator Required; TI-84 recommended
Fees

Quarters Typically Offered
Summer Day
Fall Day, Evening
Winter Day, Online
Spring Day, Evening

Designed to Serve Transfer students in mathematics, engineering and the sciences
Active Date 20170622T08:38:39

Class Limit 32
Contact Hours: Lecture 55 Lab 0 Worksite 0 Clinical 0 Other 0
Total Contact Hours 55
Degree Distributions:
AA

• Quantitative Skills
• Science

ProfTech Related Instruction
• Computation

PLA Eligible Yes

Course Outline
The course is organized into five strands:

I. Algebra

• Angles and their unit of measure.
• Convert radian to degree measures and vice versa.
• The unit circle, reference number (angle), co-terminal angles.
• Verify identities and use identities to simplify trigonometric expressions.
• Solve trigonometric equations.
• Polar coordinates:
• Change points and equations from polar coordinates to rectangular coordinates and vice versa.
• Graph points and equations in polar coordinates.
• Analyze vectors from geometric as well as analytic perspective and perform addition, subtraction, scalar multiplication, magnitude and dot product on vectors.
• Express conics in standard form and graph.

II. Trigonometric Functions

• Define trigonometric functions using right triangles and differentiate between approximate and exact values.
• Find values of the six trigonometric functions for angles using the trigonometric values of special angles.
• Graphing trigonometric functions by understanding and using:
• Domain/Range
• Period
• Amplitude and phase shifts
• Intercepts
• Describe inverse trigonometric functions along with their domain, range and graphs.

III. Communication

• Summarize and interpret mathematical information from written formats.
• Identify, extract, and organize critical information into mathematical symbols.
• Clearly communicate steps using proper terminology, symbolization, and notation.
• Demonstrate attention to detail-students will be able to analyze written material for errors and explain why they are incorrect.

IV. Problem solving

• Find arc length and area of a sector.
• Understand the difference between angular speed and linear speed.
• Solve triangles using trigonometric functions.
• Use vectors to solve static equilibrium and resultant force problems.

V. Technology-emphasis on graphing calculator

• Graph trigonometric functions in rectangular coordinates choosing the appropriate windows for viewing all details.
• Graph polar equations in polar coordinate system.
• Use calculators to approximate values of trigonometric functions and inverse trigonometric functions using radian and degree mode.

Student Learning Outcomes
Recognize and describe trigonometric functions for the unit circle and points in the rectangular coordinate system.

Apply appropriate trigonometric functions and their inverses to find angles or lengths involving right triangles.

Recognize, describe, and analyze key features of trigonometric and inverse trigonometric functions.

Apply law of sines and law of cosines to solve real-life situations involving non-right triangles.

Apply trigonometric identities and algebraic techniques to simplify trigonometric expressions.

Solve trigonometric equations.

Use basic concepts of algebraic and geometric vectors to solve elementary vector problems involving trigonometry.

Identify and graph polar functions and convert between polar and rectangular form.

Analyze and graph equations of conic sections.

Effectively use the graphing calculator to graph trigonometric and polar functions and solve trigonometric and vector equations.

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