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MATH& 142 Precalculus II • 5 Cr.




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.


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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Bellevue College
3000 Landerholm Circle SE Bellevue, WA 98007-6484 U.S.A.
Work: (425) 564-1000