Go to content
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

catcode applet
This page uses Trigonometry applets from
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

graph

A diagram showing a relationship between two variables.
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.

Full Glossary List

This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
AQA A-Level (UK - Pre-2017)C4Trigonometrypcos A + qsin A-
AQA A2 Maths 2017Pure MathsFurther TrigonometrySimplifying a cos x + b sin x-
AQA AS/A2 Maths 2017Pure MathsFurther TrigonometrySimplifying a cos x + b sin x-
CBSE XI (India)Sets and FunctionsTrigonometric FunctionsAddition identities e.g. sinx +siny sin(x+y) etc.-
CCEA A-Level (NI)C4Trigonometrypcos A + qsin A-
CIE A-Level (UK)P2Trigonometrypcos A + qsin A-
Edexcel A-Level (UK - Pre-2017)C3Trigonometrypcos A + qsin A-
Edexcel A2 Maths 2017Pure MathsTrigonometric Problem SolvingSimplifying a cos x + b sin x-
Edexcel AS/A2 Maths 2017Pure MathsTrigonometric Problem SolvingSimplifying a cos x + b sin x-
I.B. Higher Level3Trigonometrypcos A + qsin A-
Methods (UK)M2Trigonometrypcos A + qsin A-
OCR A-Level (UK - Pre-2017)C3Trigonometrypcos A + qsin A-
OCR A2 Maths 2017Pure MathsFurther Trig Identities and EquationsSimplifying a cos x + b sin x-
OCR MEI A2 Maths 2017Pure MathsFurther Trig Identities and EquationsSimplifying a cos x + b sin x-
OCR-MEI A-Level (UK - Pre-2017)C4Trigonometrypcos A + qsin A-
Pre-Calculus (US)C4Trigonometrypcos A + qsin A-
Pre-U A-Level (UK)2Trigonometrypcos A + qsin A-
Scottish (Highers + Advanced)HM3Trigonometrypcos A + qsin A-
Scottish HighersM3Trigonometrypcos A + qsin A-
Universal (all site questions)TTrigonometrypcos A + qsin A-
WJEC A-Level (Wales)C4Trigonometrypcos A + qsin A-