Pre-Calculus 30

Unit 1: Trigonometry

Angles in standard position and radians, the unit circle and six trigonometric ratios, graphs of trigonometric functions, trigonometric equations, and trigonometric identities.

• Standard position, degrees, and radians
• Coterminal angles and arc length

• The unit circle and the six ratios
• Exact values at special angles
• Solving problems with trigonometric ratios

• Graphing sine, cosine, and tangent
• Transforming trigonometric graphs

• Solving trigonometric equations algebraically
• General solutions of trigonometric equations

• Reciprocal, quotient, and Pythagorean identities
• Sum, difference, and double-angle identities

Unit 2: Functions and Transformations

Operations on and compositions of functions, transformations, reflections and inverses, logarithms, higher-degree polynomials, and radical and rational functions.

• Combining functions arithmetically
• Composing functions

• Translations and stretches of functions

• Reflecting functions
• Inverse relations and functions

• Logarithms and exponents
• Laws of logarithms
• Solving exponential and logarithmic equations
• Graphing exponential and logarithmic functions

• Polynomial division and the factor theorem
• Graphing polynomial functions
• Modelling and solving with polynomial functions

• Radical functions
• Rational functions

Unit 3: Permutations, Combinations, and the Binomial Theorem

Counting with the fundamental counting principle, permutations, combinations, and the binomial theorem via Pascal's triangle.

• The fundamental counting principle
• The permutation formula

• Combinations
• Pascal's triangle and the binomial theorem