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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.
In this lesson, students will use their previous knowledge of right triangle geometry (SOH CAH TOA) to extend understanding to the coordinate plane and trigonometric functions. Students will look at triangles on the coordinate plane, with the hypotenuse of the triangle being the radius of a circle. Each leg of the circle will be labeled x and y, respectively and this will push students to the understanding that the point on the unit circle (x,y) will be labeled as (cos (t), sin (t)).
Vocabulary: standard position, terminal ray, initial ray, reference triangle
Special Materials:
Calculator