ZaneH / precalc-book

A LaTeX book created as a final project. Created in 2015

Precalc Reference Book

Created in 2015 as a final project in high school

It's a LaTeX book containing most of what we learned in precalc

• Final.pdf - Final LaTeX output
• Reference Book.tex - Slightly outdated source code for the PDF

Contents

• Basic Functions (pg. 5)
  • Linear Function
  • Quadratic Function
  • Cubic Function
  • Reciprocal Function
  • Square Root Function
  • Exponential Function
  • Logarithmic Function
  • Sine Function
  • Cosine Function
  • Absolute Value Function
• Graphical Transformations (pg. 14)
  • Flipping the y-values over the x-axis and the y-axis
  • Moving y-values left and right on the x-axis
  • Moving the y-values up and down on the y-axis
  • Vertical modifications to the graph
    • Stretch f(x) → af(x) when a > 1
    • Shrink f(x) → af(x) when 0 < a < 1
  • Horizontal modifications to the graph
    • Stretch f(x) → f(x÷c) when c > 1
    • Shrink f(x) → f(x÷c) when 0 < c < 1
• Function Composition and Inverse (pg. 17)
  • Function Composition
  • Inverse
• Quadratic Functions (pg. 18)
  • Standard Form
  • Vertex Form
  • Converting from Standard Form to Vertex Form using Completing the Square
• Power Functions (pg. 19)
  • Direct Variation
  • Indirect Variation
• Polynomial Functions (pg. 19)
  • Multiplicity
    • Guesstimating a graph
  • Finding the function from zeros
• Long Division vs. Synthetic Division (pg. 21)
  • Long Divison Example
  • Synthetic Division Example
• Solving Inequalities With Sign Charts (pg. 22)
• Exponential and Logarithmic Functions (pg. 22)
  • Solving Exponential Functions
  • Solving Logarithmic Functions
  • Properties of Logs
    • Condensing
    • Expanding
• Partial Fraction Decomposition (pg. 23)
  • Decompose
  • Sequences and Series
    • Sequences
  • Convergent vs. Divergent Sequences
  • Sum of Finite Series
  • Partial Sum of Infinite Series
• Trigonometric Functions (pg. 24)
  • Radians
  • Unit Circle
  • Graphs of Cosecant, Secant, and Cotangent
    • Cosecant
    • Secant
    • Cotangent
  • Inverse Sine, Cosine, Tangent
    • Inverse Sine
    • Inverse Cosine
    • Inverse Tangent
  • Evaluating Trigonometry Expressions Using The Unit Circle
  • Sinusoidal Functions
• Analytic Trigonometry (pg. 31)
  • Reciprocal Identities and Quotient Identities
  • Pythagorean Identities
  • Double Angle Identities
  • Half Angle Identities
  • Power-Reducing Identities
  • Simplifying Trig Functions
  • Solving Trig Equations
  • Proving Trig Identities
  • Law of Sines
  • Law of Cosines
  • Area of a Triangle (SAS and SSS)
• Application of Trigonometry (pg. 37)
  • Vectors
  • Parametric Equation
  • Polar Coordinates
  • Graphs and Equations of Polar Relations
• Conic Sections (pg. 43)
  • Parabolas
  • Ellipse
  • Hyperbola