Transformations of Sine, Cosine and Tangent in degrees (°)

Investigating transformations of the trigonometric functions sine (y = sinx), cosine (y = cosx ) and tangent (y = tanx), with angles in degrees (°).What happens as you change the parameters A, B, C and D? Challenge yourself to find the equation of a randomly-drawn graph.

Author and programmer: Ron Barrow

UK Years 9-11, KS3, KS4, Foundation and Higher GCSE Mathematics, Grades C - A* - Data Handling, Statistics and Probability
US - Grades 7 - 10


Instructions below    This applet in German This applet in French This applet in Spanish    Waldomaths Adobe Acrobat .pdf file    See also:   General Function Transformations

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How to Use this Applet

The general sine function has the form: Asin(Bx + C) + D (similarly with cos or tan ).
The screen on this page is designed to help students understand transformations of the Sine, Cosine and Tangent functions, by experimenting with the 4 parameters (A, B, C and D). The x-axis is in degrees. You can select sine, cosine or tangent by clicking the buttons on the bottom left of the screen. If you tick the "Median Line" box then a horizontal line will be drawn in the "middle" of the function to help you understand its equation. Ticking the "Original Curve" box means that the original function remains visible while you transform it.
A challenge! - To test your understanding, hitting the "Random" button will generate a random curve. By varying the parameters, try to cover the random line with the other one, and hence find the equation of the random curve. There is usually more than one correct answer. If you want an easier start, then clicking on "1" at the top of the page will set the program so that only one of A, B, C, D changes on the random curve - the others stay the same. It get more complicated as you click "2", "3" and "4"! Have a go. If the "Easier" box is ticked, then the value of B in the random curve is never negative, which makes things a little easier.
Have some fun! Studying this function should also help understand functions and their transformations in general.