Modelling and control by Anthony Rossiter

# TRIGONOMETRY - BASIC RULES AND TYPICAL A LEVEL PROBLEMS

These videos give a quick review of the key trigonometry content on A level mathematics followed by a number of questions. The main contribution is to show how questions can be solved using simple techniques linked directly to the properties of trigonometric functions. Consequently they will be useful for students who are revising and trying to improve their problem solving skills.

The videos do spend a little time demonstrating that some key results are true, but students could skip those parts and concentrate on the worked solutions if they want too. Use the left hand toolbar to access the other chapters and themes. It is implicit that for many engineering topics, students have core competence in some mathematical topics such as polynomials, roots, complex numbers, exponentials, logarithms and Laplace. This section contains the following topics. Under each topic there are hardcopy (pdf) notes, a video talk through of key derivations with example problems and also a tutorial sheet for users to test themselves.

## Revision of A level trigonometry - questions and answers 1

A rapid review of the core rules which students learn in GCSE such as SOH, CAH, TOA, sine rule, cosine rule, areas of triangles and Pythagoras.

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.

#### Quick test question

What information indicates the use of the sine rule is appropriate.
A. Knowledge of 2 angles and a side.
B. Knowledge of 2 sides and the angle between them.
C. Knowledge of 3 sides..
D. None of the above.

## Revision of A level trigonometry - questions and answers 2

Gives a general definition for the sine function and shows how this can be plotted for angles outside of 0 to 90 degrees. Uses the sketch of the sine function to show how problems involving sine can have multiple solutions, and demonstrates with several worked examples how these multiple solutions are easy to compute. Questions start around 12 minutes into video.

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.

#### Quick test question

Given that sin(105)=a, what other angles have the same value for sine?
A. 255, 475,... .
B. 75, 435,... .
C. -75, 295, ... .
D. None of the above.

## Revision of A level trigonometry - questions and answers 3

Gives a general definition for the cosine function and shows how this can be plotted for angles outside of 0 to 90 degrees. Uses the sketch of the cosine function to show how problems involving cosine can have multiple solutions, and demonstrates with several worked examples how these multiple solutions are easy to compute. Questions start around 9 minutes into video.

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.

## Revision of A level trigonometry - questions and answers 4

Gives a general definition for the tangent function and shows how this can be plotted for angles outside of 0 to 90 degrees. Uses the sketch of the tangent function to show how problems involving tangent can have multiple solutions, and demonstrates with several worked examples how these multiple solutions are easy to compute. Questions start around 10 minutes into video.

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.

## Revision of A level trigonometry - questions and answers 5

Introduces radians as a means of measuring angle. Gives a number of example problems to demonstrate how the problems tackled in videos 2-4 can equally be solved in radians rather than degrees. Questions start around 3 minutes into video.

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.

## Revision of A level trigonometry - questions and answers 6

Looks at links between Pythagoras and sine/cosine and gives a number of numerical examples showing how this link can be exploited to solve algebraic problems that commonly appear on A level papers. Questions start almost immediately.

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.

#### Quick test question

What is the relationship between degrees and radians?
A. 150degrees = 2/3 pi radians.