Graphs of Trig Functions
This interactivity takes a look at the graphs of the trig functions. First of all, take a look at the unit circle in the top half of the activity. You can change the angle θ using the slider. This will move the point P round the circle. Deselect "Show Algebra" to get the actual values.
What is the length of OP?
How is the point N generated?
Now look at the bottom half of the activity. How does the blue point relate to the top half of the activity?
(HINT: look at the blue dashed line)
What function is represented by the blue graph (select Show Trace 1 to sketch the graph as you move the point).
Now investigate what Function 2 and Function 3 are.
What is the length of OP?
How is the point N generated?
Now look at the bottom half of the activity. How does the blue point relate to the top half of the activity?
(HINT: look at the blue dashed line)
What function is represented by the blue graph (select Show Trace 1 to sketch the graph as you move the point).
Now investigate what Function 2 and Function 3 are.
Ideas for Teachers
Although this activity could be used directly by the pupils,it is designed for use at the front of the classroom on a projector. This activity demonstrates the link between the unit circle and the trig functions, and as such is a good introduction to the graphs. You have the option of working purely algebraically, or choosing to use the actual values with the "Show Algebra" checkbox. You can also choose to have the trace visible or not (which will plot the graph, not just show the current point).
This activity does not go beyond 360°, which is the natural progression from here. A question like "What happens at 361°" should get them thinking.
Although this activity could be used directly by the pupils,it is designed for use at the front of the classroom on a projector. This activity demonstrates the link between the unit circle and the trig functions, and as such is a good introduction to the graphs. You have the option of working purely algebraically, or choosing to use the actual values with the "Show Algebra" checkbox. You can also choose to have the trace visible or not (which will plot the graph, not just show the current point).
This activity does not go beyond 360°, which is the natural progression from here. A question like "What happens at 361°" should get them thinking.
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