# STEP 3 Hyperbolic Functions

### 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.

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 $(a+bi)^2=a^2 - b^2 +2abi$.

Assignment PDF:
Topic Notes:
Solution:

Underground Mathematics: Selected worked STEP questions

STEP Question database

University of Cambridge Mathematics Faculty: What do we look for?

University of Cambridge Mathematics Faculty: Information about STEP