Reflection: Complex Tasks Triangles That Are Wrong Because They Are Not Right - Section 2: Share


At this point in our study of trigonometry I always have to fight the battle of making a new right triangle using the reference angle. As seen in this diagram, most students were doing that to find the coordinates of point B in question #4. I completely understand why students do it, but I start to fight this battle so they will see the connection when we study the trig form of a complex number or polar coordinates.

The main thing I have to tell them is that if they use the cosine of 122 degrees instead of 58 degrees, then their coordinate will automatically be the correct sign, and they will not have to convert it from positive to negative. It took some work, but students finally realized that the coordinates for point B are (7cos122°, 7sin122°) and there would be no need at all for the 58° angle. Furthermore, we generalized this relationship for any point. The coordinates could be (rcosθ, rsinθ) where r is the radius and θ is the angle measure.

  Complex Tasks: Resist the Urge to Make a New Triangle
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Triangles That Are Wrong Because They Are Not Right

Unit 6: Additional Trigonometry Topics
Lesson 1 of 12

Objective: SWBAT derive and apply the Law of Cosines.

Big Idea: Investigate how to find side lengths and angle measures for non-right triangles.

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