Trigonometric Graphs

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This resource contains two interactive excel files dealing with the graphs of trigonometric functions.

Trigonometry: X=cos, Y=sin
The first three interactive sheets make use of a point on a unit circle to illustrate the relationship between the angle (turned clockwise or anticlockwise from the positive x axis) and the coordinates of the point. Each sheet has a picture of the circle, the angle and the coordinates expressed as sine or cosine of the angle and as a decimal.

The next sheet shows the graphs of sine and cosine and students need to use inverse trig functions to find the two values of the angle in the range 0⁰ to 360⁰. This is followed by a similar sheet where the graphs are for sine and cosine of angles in the range -180⁰ to +180⁰. The final interactive sheets deal with the 3 trig ratios for the special angles 30⁰, 60⁰ and 45⁰ and their associated angle on the unit square.

There are a further five sheets of questions which may be suitable for use in the classroom.

Modelling: Depth of Water in a Tidal River
This interactive excel program develops a model for depth of water in a tidal river based upon the sine curve. The first interactive sheet shows a cycle once or twice every 360 days. This is followed by a similar sheet showing the graph and formula for a cycle every 24 or 12 hours.

The sheet entitled "Tidal River" allows students to explore the graph of the water depth as they alter three parameters; the mean depth of water, the time of high tide and the difference between high and low tide. Students are able to reveal the function for this model.

The final interactive sheet allows students to explore the functions involved in the model and see the graph of these functions in the form D=asin[30(t-b)]+c.

There are a further five sheets of questions which may be suitable for use in the classroom.


This program was designed by be viewed on a screen with a resolution of 1024 x 768. Users may have to adjust the resolution of their screen for the pages to display as was originally intended. The program uses macros which need to be enabled on users' machines..

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