Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: Calculus II
Topic: Transcendental Functions
Subtopic: Hyperbolic Trigonometric Functions

Overview

Trigonometric functions are defined on a triangle. Similarly hyperbolic trig functions are defined on a hyperbola. They can be expressed in terms of exponential functions thus they tie trigonometric functions, exponential functions, and conic sections together. Very cool stuff!

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 5.3.1 Define the hyperbolic sine and cosine functions in terms of e
• 5.3.2 Define the other four hyperbolic trig functions in terms of sinh(x) and cosh(x)
• 5.3.3 Graph all six hyperbolic trig functions
• 5.3.4 Evaluate hyperbolic trig functions by hand and electronically
• 5.3.5 Understand relationships between the six hyperbolic trig functions
• 5.3.6 Simplify expressions containing hyperbolic trig functions using identities
• 5.3.7 Prove hyperbolic trig identities
• 5.3.8 Find limits of hyperbolic trig expressions graphically and algebraically
• 5.3.9 Differentiate hyperbolic trig functions
• 5.3.10 Integrate hyperbolic trig functions
• 5.3.11 Solve application problems involving hyperbolic trig functions

Terminology

Terms you should be able to define: hyperbolic trig functions, sinh(x), cosh(x), tanh(x), csch(x), sech(x), coth(x)

Mini-Lectures and Examples

Supplemental Resources (required)