### Introduction

This STEP support module introduces the small angle approximations for $\sin \theta$, $\cos \theta$ and $\tan \theta$ and asks some questions about coordinate geometry. Previous assignments can be found here, but you can do this one without having done the others first.

STEP questions are difficult, they are supposed to be and you should expect to get stuck. However, as you tackle more and more STEP questions you will develop a range of problem solving skills (and spend less time "being stuck").

### About this assignment

The assignment is published as a pdf file below. Each STEP Support assignment module starts with a warm-up exercise, followed by preparatory work leading to a STEP question. Finally, there is a warm-down exercise.

The **warm up** for this assignment derives the small angle approximations for $\sin \theta$, $\cos \theta$ and $\tan \theta$ (which hold when $\theta$ is in radians).

The **main STEP question (2005 STEP 1 Question 6)** is about coordinate geometry and describing a path of a point.

The **final question** has a couple of probability problems for you to solve.

There is more on the Monty Hall problem here including a nice simulator. A nice introduction to Bayes' theorem is given in this Plus maths article.

### Hints, support and self evaluation

The **“Hints and partial solutions for Assignment 19”** file gives suggestions on how you can tackle the questions, and some common pitfalls to avoid, as well as some partial solutions and answers.

Here is a Worked Video Solution to the STEP question from this assignment.