THE GRAPH OF f(θ) = sin(θ)

The Interactive Graph below needs the Java Plugin for your browser. Download it here. The plugin is perfectly safe. If you do NOT have the plugin you will not see the interactive graph within a large rectangle below the directions.

Please start with the video tutorial on the right to get some insight into the interactive Graph below.

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DIRECTIONS
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Below is the function f(θ) = sin (θ) which is constructed using the UNIT CIRCLE.

- You will see a red point that you can manipulate with your mouse. You can drag the red point along the curve and see the points θ value "projected" along the horizontal - axis and the Y VALUE FROM THE UNIT CIRCLE "projected" along the vertical axis.

- Also, by right clicking your mouse on the graph you will bring up a menu system that allows you to adjust the Cartesian Coordinate System on which the interactive graph sits.

- Your goal is to be able to do the following:

a) Determine the domain by moving the red point and examining the projection of the θ coordinate along the horizontal axis.
b) Determine the range by moving the red point and examining the projection of the Y VALUE FROM THE UNIT CIRCLE along the vertical axis.
c) Determine on what intervals of θ the function f(θ) will be increasing or decreasing.