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Warm-up (4 m)

Warm-up (4 m). For problems 1 – 2, sketch each graph. Then find the domain and range of each graph. 1. f(t) = 3sin(2t – π) 2. f(t) = –2cos(t) + 4. f(t) = 3sin(2t – π). f(t) = –2cos(t) + 4. Introduction to the Tangent Graph. Tangent Investigation. Remember:

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Warm-up (4 m)

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  1. Warm-up (4 m) For problems 1 – 2, sketch each graph. Then find the domain and range of each graph. 1. f(t) = 3sin(2t – π) 2. f(t) = –2cos(t) + 4

  2. f(t) = 3sin(2t – π)

  3. f(t) = –2cos(t) + 4

  4. Introduction to the Tangent Graph

  5. Tangent Investigation • Remember: • Fill out a table for the five key points using the formula for tangent and the unit circle • Then answer the reflection question

  6. Tangent Table

  7. Observations? • What happens to the graph of tangent at and ? discontinuities in the graph • The graph of tangent has vertical asymptotes at those two points.

  8. The Tangent Graph

  9. Think-Pair-Share • What do you think is the period of f(t) = tan(t)? π • What do you think is the amplitude of f(t) = tan(t)? Why? DNE because of the vertical asymptotes • What do you think is the range of f(t) = tan(t)? (–∞, ∞)

  10. Think-Pair-Share, cont. • What do you think is the domain of f(t) = tan(t)? where n is any integer (the domain excludes and any multiples of )

  11. Transformations of Tangent • Because tangent graphs don’t have an amplitude, they follow the format f(t) = tan(bt – c) + d

  12. Examples

  13. Your Turn: • Complete problems 1 – 3 in guided notes. 1. 2. 3.

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