## Reflection: Staircase of Complexity Does cos(A - B) = cos(A) - cos(B)? - Section 2: Explore

The go-to strategy for thinking about whether cos(A - B) = cos(A) - cos(B) was to plug in unit circle values and see if it would work. This student did a really nice job of testing some specific values and explaining why it did not work. Not many students thought about it on a conceptual level, but I did hear one group discussing how you could not distribute cosine to both terms.

This student work was also enlightening but it shows just how difficult this trigonometry notation can be. The student wrote "cos(1/2 -  - 1/2)" even though she already took the cosine of the angles to get the ratios 1/2 and -1/2. This was a good reminder to me that the notation is something that continually needs to be reinforced with students.

Staircase of Complexity: Finding a Counterexample

# Does cos(A - B) = cos(A) - cos(B)?

Unit 5: Trigonometric Relationships
Lesson 4 of 15

## Big Idea: Students disprove a potential identity and then derive the real cos(A - B) formula.

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Standards:
Subject(s):
Math, Precalculus and Calculus, Trigonometry, trigonometric functions (Simplifying), trigonemetric identities, sum and difference formulas, Trigonometric Equations
50 minutes

### Tim Marley

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