Two simple
trigonometrical curves can be added to produce one combined graph. When you
click on

**Start**, the graphs of a \sin(bx+c) and d \cos(ex+f) are plotted, together with, at the bottom, the graph of a \sin(bx+c) + d \cos(ex+f) . Experiment with different values for these six constants. When is the combined graph a basic sine (or cosine) wave?## Summary/Background

As long as the values of the constants b and d are equal, the combined graph is a basic sine or cosine wave. In other words, if two trig functions have the same frequency than their sum will be a sine wave.

## Software/Applets used on this page

This page uses Trigonometry applets from

catcode.com

catcode.com

## Glossary

### cosine

The trigonometrical function defined as adjacent/hypotenuse in a right-angled triangle.

### frequency

Of a function: the rate of repetition of a periodic function.

In statistics: the number of occurances of a value

In statistics: the number of occurances of a value

### graph

A diagram showing a relationship between two variables.

The diagram shows a vertical y axis and a horizontal x axis.

The diagram shows a vertical y axis and a horizontal x axis.

### sine

The trigonometrical function defined as opposite/hypotenuse in a right-angled triangle.

### trigonometry

The study of the relationships between the angles and sides of triangles.

## This question appears in the following syllabi:

Syllabus | Module | Section | Topic | Exam Year |
---|---|---|---|---|

AQA A-Level (UK - Pre-2017) | C4 | Trigonometry | pcos A + qsin A | - |

AQA A2 Maths 2017 | Pure Maths | Further Trigonometry | Simplifying a cos x + b sin x | - |

AQA AS/A2 Maths 2017 | Pure Maths | Further Trigonometry | Simplifying a cos x + b sin x | - |

CBSE XI (India) | Sets and Functions | Trigonometric Functions | Addition identities e.g. sinx +siny sin(x+y) etc. | - |

CCEA A-Level (NI) | C4 | Trigonometry | pcos A + qsin A | - |

CIE A-Level (UK) | P2 | Trigonometry | pcos A + qsin A | - |

Edexcel A-Level (UK - Pre-2017) | C3 | Trigonometry | pcos A + qsin A | - |

Edexcel A2 Maths 2017 | Pure Maths | Trigonometric Problem Solving | Simplifying a cos x + b sin x | - |

Edexcel AS/A2 Maths 2017 | Pure Maths | Trigonometric Problem Solving | Simplifying a cos x + b sin x | - |

I.B. Higher Level | 3 | Trigonometry | pcos A + qsin A | - |

Methods (UK) | M2 | Trigonometry | pcos A + qsin A | - |

OCR A-Level (UK - Pre-2017) | C3 | Trigonometry | pcos A + qsin A | - |

OCR A2 Maths 2017 | Pure Maths | Further Trig Identities and Equations | Simplifying a cos x + b sin x | - |

OCR MEI A2 Maths 2017 | Pure Maths | Further Trig Identities and Equations | Simplifying a cos x + b sin x | - |

OCR-MEI A-Level (UK - Pre-2017) | C4 | Trigonometry | pcos A + qsin A | - |

Pre-Calculus (US) | C4 | Trigonometry | pcos A + qsin A | - |

Pre-U A-Level (UK) | 2 | Trigonometry | pcos A + qsin A | - |

Scottish (Highers + Advanced) | HM3 | Trigonometry | pcos A + qsin A | - |

Scottish Highers | M3 | Trigonometry | pcos A + qsin A | - |

Universal (all site questions) | T | Trigonometry | pcos A + qsin A | - |

WJEC A-Level (Wales) | C4 | Trigonometry | pcos A + qsin A | - |