# MATH& 142Precalculus II• 5 Cr.

## Description:

Prepares students for the MATH& 151/152/153 calculus sequence. Students work intensively with functional trigonometry, polar coordinates, translation and rotation of axes, plane analytic geometry, lines and planes in space, and non-linear systems. Fulfills the quantitative or symbolic reasoning course requirement at BC. Prerequisite: Placement by assessment, or MATH& 141 with a C- or better.

## Outcomes:

After completing this class, students should be able to:

• to understand measuring angles in Degrees and in Radians and to do conversions between Degrees and Radians
• to convert between angles measured in Degrees,Minutes,Seconds andthose measured in Decimal Degrees
• to use Arc Length Formula for a Circle
• to know Basic Trig Definitions relative to a Right Triangle
• to know and use the Special Angle values of 30-60-90 and 45-90 degree Triangles
• to know Basic Trig Identities relating Sine to Cosine, Tangent to Sine and Cosine, and reciprocal Trig Definitions to Sine,Cosine, and Tangent
• to know Trig Definitions extended to four Quadrants and Reference Angles
• to use a Graphics Calculator and its Trig keys and Inverse Trig keys
• to solve Right Triangle Application Problems
• to extend evaluation of Trig values to any Real number using the Unit Circle Definitions for Trig values
• to know Periodic Properties of Trig Functions and Negative Angle Properties
• to graph Sine and Cosine Graphs using Amplitude, Period, Phase Shift,and Vertical Shift and to recognize these as an example of general functionshifting,stretching, and reflecting properties
• to graph Tangent, Cotangent, Secant, and Cosecant Graphs
• to use a Graphics Calculator for graphing individual Trig Functions aswell as for Graphical Addition and for graphing Damped Sine and CosineGraphs
• to recognize and solve Simple Harmonic Motion Application Problems
• to use Deductive Proofs to verify Trig Identities and to use Counterexamples to Disprove false Trig Identities
• to solve Trig equations and Applications
• to use certain Trig Identities such as the Add and Subtract Laws, Linear Combinations of Sines and Cosines, Double Angle and Multiple Angle, as well as Half-Angle
• to use Factor Formulas or Sum to Product Formulas
• to understand Inverse Trig functions including Definitions, Graphs, and Properties
• to solve Non-Right Triangles (including finding their Area) and related Applications with Law of Sines and Law of Cosines
• to understand the concept of a 2-dimensional vector, related graphing of vectors, notation and properties of vectors, and the use of vectors in solving Applications
• to have a brief intro to Dot Product and Perpendicularity as well as Angle between vectors
• to understand the Ellipse and the Hyperbola cases of the Conic Sections including Definitions, Graphs, and Applications
• to understand Parametric Equations and Plane Curves including Definitions, Graphs, Applications (e.g. Cycloid) and how to apply the capabilities of a Graphics Calculator to greatly expand one’s ability inthese topics
• to understand Polar Coordinates including Definition, Conversion with Rectangular Coordinates, Polar Functions and their Graphs and how to apply the capabilities of a Graphics Calculator to greatly expand one’s ability in these topics
• to understand, if time permits in the quarter, some of the following topics:
• Complex Numbers: Graphing and Trigonometric(Polar) Form, DeMoivre’s Theorem and Nth Powers and Roots of Complex Numbers or
• Handout: 3-dimensional Coordinates and Vectors, Equation of a Plane and Graphing Planes as well as Equations of Lines and Graphing Lines in 3-dimensions or
• Rotation of Axes: Formulas, Usage with Graphing Rotated Conic sections.

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