The Unit Circle (Lesson 4.3 Day 1)

Unit 4 - Day 4

​Learning Objectives​
  • Use the legs of special right triangles with hypotenuse of 1 to find ordered pairs on the unit circle at key angles.

  • Use reference angles to explain the symmetry of the unit circle in the four quadrants.

Quick Lesson Plan
Activity: Coming Full Circle

     

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Lesson Handout

Answer Key

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Experience First

In numbers 1 and 2, the students will write ratios for sine and cosine when given a triangle with all of the side lengths.  We want them to see that when the hypotenuse is 1, the actual side length of the triangles are the same as the sine and cosine ratios for specific angles.  This will lead them to the unit circle, where the radius is 1 and the values of sine and cosine at different angles are equal to the x- and y-coordinates at those spots.  The idea here is that students don’t get caught up in “Sine = y and cosine = x,” but they keep up with the understanding that sine is the ratio of the opposite side to the hypotenuse and cosine is the ratio of the adjacent side to the hypotenuse.  In number three, they’ll develop the understanding of the first quadrant of the unit circle as it relates to evaluating sine, cosine, and tangent of different angles.

Formalize Later

The sequencing of questions in this lesson was developed strategically so the students would understand the concept behind “the unit circle” and how it helps us evaluate trigonometric ratios for specific angles.  Again, it’s important that students understand why the cosine is the x-coordinate and the sine is the y-coordinate, so be sure to keep referring back to the ratios from the triangles throughout the debrief.  Show them how to extend their knowledge to eagles like 0 degrees and 90 degrees so that they’ll be prepared for looking at angles greater than 180 degrees or less than 0 degrees in the next lesson.

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