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Big Ideas:
The unit circle has a radius of 1, so sin (t) =y/1=y and cos(t) =x/1=x and any point on the unit circle (x, y) can be labeled (cos(t),sin(t)). Therefore cos(t) and sin(t) can be evaluated using the reference triangles derived from Pythagorean Theorem.
A trigonometric ratio is a function that has a domain and can be graphed using the terminal ray of the unit circle. The sine and cosine functions have a period of 2pi and an amplitude of 1. The tangent graph is undefined at positive or negative pi/2 and has a period of pi .
This lesson builds on student understanding of the graphs of the trigonometric functions. The task pushes students to use their knowledge of the unit circle to create a graph for the tangent function. The lesson builds toward the understanding of application based problems that come later in the lesson sets.
Special Materials:
graph paper