# Trigonometry resources

### Guides (1)

Just the Maths (A.J.Hobson)

"Just the Maths" authored by the late Tony Hobson, former Senior
Lecturer in Mathematics of the School of Mathematical and
Information Sciences at Coventry University, is a collection of separate mathematics units, in chronological
topic-order, intended for foundation level and first year
degree level in higher education where mathematics is a service discipline e.g. engineering.

### iPOD Video (1)

Trigonometric ratios for any angle - an Animation

Video for iPod.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

### Quick Reference (6)

Degrees and radians

This leaflet explains how angles can be measured both in degrees and in radians.
It explains how to convert from degrees to radians and vice-versa. (Engineering Maths First Aid Kit 4.1)

Graphs of the trigonometric functions

This leaflet gives graphs of the functions
sine, cosine and tangent and notes some important properties. (Engineering Maths First Aid Kit 4.3)

Pythagoras' theorem

This leaflet reminds students of Pythagoras' theorem and gives some simple examples. (Engineering Maths First Aid Kit 4.5)

The sine rule and cosine rule

This leaflet states the sine and cosine rules and gives examples of their use. (Engineering Maths First Aid Kit 4.6)

The trigonometrical ratios

This leaflet defines sine, cosine and tangent of angles in a right-angled triangle and gives some standard ratios. (Engineering Maths First Aid Kit 4.2)

Trigonometrical identities

This leaflet lists a number of commonly used trigonometrical identities. (Engineering Maths First Aid Kit 4.4)

### Teach Yourself (11)

a cos x +b sin x = Rcos(x-a)

In this unit we explore how the sum of two trigonometric functions can be expressed as a single trigonometric function.

Cosecant, Secant and Cotangent

This unit explains what is meant by these three trigonometric ratios.
Graphs of the corresponding functions are provided.

Pythagoras' theorem

This unit states Pythagoras' theorem and illustrates its use in the solution of two- and three-dimensional problems.

Sine, cosine and tangent of an angle of any size

This unit explains how we define the trig ratios sine, cosine, and tangent for an angle of arbitrary size.

The double angle formulae

This unit looks at the trigonometric formulae known as the double angle formulae.

Triangle formulae

This unit explains the sine rule, cosine rule and formula for finding the area of a triangle.

Trigonometric equations

This workbook explains how a number of trigonometric equations can be solved by making reference to a Table of standard results and using the symmetries and periodicities present in the graphs of trig functions.

Trigonometric identities

In this unit several identities are derived and then used in the solution of trigonometric equations.

Trigonometrical ratios in a right angled triangle

This unit introduces the ratios sine, cosine and tangent, with reference to a right angled triangle.

### Test Yourself (23)

Diagnostic Test - Pythagoras' theorem

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Diagnostic Test - R cos (x minus alpha)

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Diagnostic Test - Radians

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Diagnostic Test - Solving Trigonometric Equations

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Diagnostic Test - The addition formulae

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Diagnostic Test - The double angle formula

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Diagnostic Test - Triangle Formulae

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Diagnostic Test - Trigonometric functions: cosec. sec. cot

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Diagnostic Test - Trigonometric identities

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Diagnostic Test - Trigonometric Ratios 1

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Diagnostic Test - Trigonometric Ratios 2

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - Pythagoras' Theorem

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - Radians

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - Solving Trigonometric Equations

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - The Addition Formulae

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - The Double Angle Formula

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - The form R cos(x minus alpha)

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - Triangle Formulae

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - Trig functions: cosec. sec. cot

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - Trigonometric identities

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - Trigonometric Ratios 1

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - Trigonometric Ratios 2

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Maths EG

Computer-aided assessment of maths, stats and numeracy from GCSE to undergraduate level 2. These resources have been made available under a Creative Common licence by Martin Greenhow and Abdulrahman Kamavi, Brunel University.

### Third Party Resources (2)

Mathematics Support Materials from the University of Plymouth

The output from this project is a library of portable, interactive, web based support packages to help students learn various mathematical ideas and techniques and to support classroom teaching.

There are support materials on ALGEBRA, GRAPHS, CALCULUS, and much more.

This material is offered through the mathcentre site courtesy of Dr Martin Lavelle and Dr Robin Horan from the University of Plymouth.

**Support material from the University of Plymouth:**

The output from this project is a library of portable, interactive, web based support packages to help students learn various mathematical ideas and techniques and to support classroom teaching.

There are support materials on ALGEBRA, GRAPHS, CALCULUS, and much more.

This material is offered through the mathcentre site courtesy of Dr Martin Lavelle and Dr Robin Horan from the University of Plymouth.

University of East Anglia (UEA) Interactive Mathematics and Statistics Resources

The Learning Enhancement Team at the University of East Anglia (UEA) has developed la series of interactive resources accessible via Prezi mind maps : Steps into Numeracy, Steps into Algebra, Steps into Trigonometry, Bridging between Algebra and Calculus, Steps into Calculus, Steps into Differential Equations, Steps into Statistics and Other Essential Skills.

### Video (14)

Hyperbolic functions - David Saunders

This mathtutor extention video explains the derivation of hyperbolic functions starting from two-dimensional space. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Pythagoras' theorem

Pythagoras theorem - the square on the hypotenuse is equal to the sum of the squares on the other two sides - is well known. In this tutorial we revise the theorem and use it to solve problems in right-angled triangles. A less familiar form of the theorem is also considered. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Pythagoras' Theorem - an Animation

This mathtutor animation shows visually that the square on the hypotenuse is equal to the sum of the squares on the other two sides. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Radian measure

Most people usually learn to measure an angle in degrees. But in many scientific and engineering calculations radians are used in preference to degrees.
(Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Sine, cosine and tangent of an angle of any size

Knowledge of the trigonometric ratios sine, cosine and tangent is vital in many fields of engineering, maths and science. This unit explains how the sine, cosine and tangent of an arbitrarily sized angle can be found. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Solving trigonometrical equations

The strategy we adopt in solving trigonometric equations is to find one solution using knowledge of commonly occurring angles and then use the symmetries in the graphs of the trigonometric functions to deduce additional solutions. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

The addition formulae

There are six so-called addition formulae often needed in the solution of trigonometric problems. In this unit we start with one and derive a second. Then we take another one as given and derive a second one from that. Finally we use these four to help us derive the final two. (Mathtutor Video Tutorial)

The double angle formulae

Double angle formulae are so called because they involve trigonometric functions of double angles e.g. sin 2A, cos 2A and tan 2A. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

The form Rcos(x-a)

In this unit we explore how the sum of two trigonometric functions e.g.3 cos x plus 4 sin x, can be expressed as a single trigonometric function. Having the ability to do this enables us to solve trigonometric equations and find maximum and minimum values. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Triangle formulae

A common mathematical problem is to find the angles or lengths of the sides of a triangle when some, but not all, of these quantities are known. It is also useful to be able to calculate the area of a triangle from some of this information. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Trig functions: cosecant, secant and cotangent

In this unit we see how the three trigonometric ratios cosecant, secant and cotangent can appear in trigonometric identities and in the solution of trigonometric equations. Graphs of the functions are obtained from a knowledge of sine, cosine and tangent. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Trig ratios in a right angled triangle

Knowledge of the trigonometric ratios of sine, cosine and tangent is vital in very many fields of engineering, science and maths. This unit introduces them and provides examples of how they can be used to solve problems. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Trigonometric identities

In this unit we consider trigonometric identities and how to use them to solve trigonometric equations. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Trigonometric ratios of an angle of any size - an Animation

This mathtutor animation shows how graphs of sin, cos and tan may be plotted as angles increase in positive and negative directions. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.