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STEP Support Programme

STEP 3 Hyperbolic Functions *Updated*

Introduction

This module contains STEP 3 questions on Hyperbolic Functions.

Each STEP 3 module consists of 4 STEP questions, some topic notes and useful formulae, a "hints" sheet and a "solutions" booklet.

STEP questions are challenging, so don't worry if you get stuck. These STEP 3 modules assume that you have already begun to develop your problem-solving skills and approach to STEP questions by working on the Foundation modules and the STEP 2 modules. You can also ask for support, help and hints on the STEP Support discussion forum.

About this assignment

Hyperbolic functions are related to the Trigonometric functions, and they can be expressed rather nicely in terms of exponentials. They often appear in Calculus questions (such as Questions 1, 2 and 3 of this module).

Question 3 asks for a proof which can be done by induction. See Foundation Assignment 20 for an introduction to proof by induction. For Question 4 you need a little knowledge of complex numbers, i.e. $i^2=-1$, $\sqrt{-3}=i\sqrt{3}$ and $(a+bi)^2=a^2 - b^2 +2abi$.