Trigonometry Overview

Trigonometry is a branch of mathematics focusing on relationships between the sides and angles of triangles. It is foundational to Geometry, Algebra, and Calculus.

Key Topics Covered

1. Understanding How Angles Are Measured

   • Degrees: A full circle is 360 degrees. Mainly used to describe angle sizes.
   • Radians: One revolution is (2\pi) radians. Used in most computations.
   • Unit Circle: Circle with a radius of 1 centered at the origin; fundamental in defining trigonometric ratios.
   • Practice problems and solutions are provided.

2. Trigonometric Functions

   • Definitions: Six trigonometric functions relate angles of a right triangle to its side lengths: sine, cosine, tangent, cosecant, secant, cotangent.
   • Trigonometric Ratios: Explained using the mnemonic SOH-CAH-TOA.
   • Methods to find values of trigonometric functions and missing side lengths using given angle measures.
   • Practice problems and solutions are provided.

3. Using Definitions and Fundamental Identities

   • Reciprocal, Quotient, and Pythagorean Identities: Basic identities essential for simplifying expressions and solving equations.
   • Sum and Difference Formulas: Used to calculate values for specific angle sums or differences.
   • Double and Half Angle Formulas: Calculate angles that are double or half of a given angle.
   • Product to Sum and Sum to Product Formulas: Convert product of functions into sums and vice versa.
   • Law of Sines and Cosines: Solve oblique triangles (non-right triangles).
   • Practice problems and solutions are provided.

4. Key Features of Graphs of Trig Functions

   • Sine, Cosine, and Tangent Graphs: Understanding periodicity, domain, range, intercepts, and symmetry.
   • Amplitude and Period: Amplitude indicates the height from the midline of the wave; period is the distance required for the function to complete one full cycle.
   • Phase and Vertical Shifts: Transformations shifting functions left, right, up, or down.
   • Graphing using technology such as calculators and Desmos.
   • Practice problems and solutions are provided.

Additional Resources

• Khan Academy videos are referenced throughout for visual and step-by-step guidance.
• Practice problems at the end of each section to reinforce understanding.

This overview serves as a fundamental guide to trigonometry, essential for further studies in mathematics like Calculus.