Reflection: Developing a Conceptual Understanding Introduction to Sine and Cosine - Section 3: Review Big Conceptual Ideas Behind Trigonometry and its Notation

 

Thinking beyond procedures is absolutely critical in this unit.  I have found that this particular idea—what does the sine, cosine, or tangent of a particular angle mean?—so important, yet so hard for students to make sense of with regard to similar triangles.

This year, I decided to have students work in pairs.  Last year, I had students work individually as they drew a couple of examples of triangles that fit the given trig ratios, which worked for some students, but not for all.  This year, I decided to pair students up and have them take turns.  One partner would draw (1) a right triangle, (2) label one side a particular length, and (3) indicate the reference angle.  Then their partner would have to label the appropriate side with a length that fit the criteria his/her partner had specified.  Great questions and discussion came from this decision!

  Increasing Engagement and Conceptual Understanding Through Pair Talk
  Developing a Conceptual Understanding: Increasing Engagement and Conceptual Understanding Through Pair Talk
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Introduction to Sine and Cosine

Unit 12: Triangle Similarity and Trigonometric Ratios
Lesson 6 of 11

Objective: Students will be able to solve problems by using the relationship between the sine and cosine ratios of complementary angles.

Big Idea: Students will reinforce their understanding of the definition of trigonometric ratios by drawing several examples of triangles that satisfy a particular ratio and explaining the ratio's meaning.

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Subject(s):
Math, Geometry, Trigonometry, sine, cosine
  87 minutes
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