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S = contains supplemental resources
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

Define: hyperbolic trig functions, sinh(x), cosh(x), tanh(x), csch(x), sech(x), coth(x)

Supplemental Resources (optional)

Supplemental Resources (required)