PreCalculus

 

PreCalculus

Trigonometry, identities, polar equations, logarithms, sequences, limits and other topics to prepare for calculus.

Major Concepts and Skills Include:

  • Understanding and working with trigonometric ratios, their reciprocals, and their inverses
  • Working with trigonometric expressions and identities
  • Understanding and working with polar coordinates and radian measure
  • Graphing and analyzing trigonometric functions
  • Understanding functions, limits, domain, and range
  • Working with Arithmetic and Geometric Series and Sequences

Additional Concepts and Skills:

  • Understanding and applying the Laws of Sines and Cosines
  • Understanding and applying the Sum, Difference, Double-Angle, and Half-Angle Identities
  • Proving trigonometric identities
  • Working with vectors and adding linear functions
  • Understanding and working with logarithms
  • Working with Euler's number and natural logarithms

Checklist for Success

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Explore PreCalculus's Scope and Sequence

Table of Contents:

  • Pythagorean Theorem
  • Special Right Triangles (30°- 60°- 90° and 45°- 45°- 90°)
  • Trigonometric Ratios
  • Inverse Trigonometric Ratios
  • Interpreting the Trigonometry Tables
  • Using the Trig. Table to Solve for the Unknown
  • Using a Calculator and Arc Functions
  • Angles of Elevation and Depression
  • Angles less than 0°
  • Angles greater than 360°
  • Reference Angles
  • Cofunctions
  • Negative Angle Relationships
  • Proving Trigonometric Identities
  • Sum and Difference Identities
  • Double-Angle and Half-Angle Identities
  • Law of Sines
  • Law of Cosines
  • Ambiguity in the Law of Sines
  • Radian Measure
  • Polar Coordinates and Rectangular Coordinates
  • Polar Equations and Polar Graphs
  • Vectors
  • Functions: Relation, Domain, and Range
  • Graphing the Sine and Cosine Functions
  • Graphing the Secant and Cosecant Functions
  • Graphing the Tangent and Cotangent Functions
  • Logarithms
  • Arithmetic Sequences and Series
  • Geometric Sequences and Series
  • Proof of Cos (A - B) = Cos A Cos B + Sin A Sin B
  • Finding the Area of a Triangle Trigonometrically
  • Interpolation
  • Navigation
  • Natural Logarithms
  • Equations with Absolute Value
  • Equations with Radicals
  • Inequalities with Absolute Value
  • Inequalities with Radicals
  • Limits
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