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Chapter 4.5 Graphs of Tangent, Cotangent, Secant, and Cosecant

Chapter 4.5 Graphs of Tangent, Cotangent, Secant, and Cosecant. Learning Target: I can generate the graphs for tangent, cotangent, secant, and cosecant. Tangent Function. f(x) = tan (x) D: all real numbers except odd multiples of П /2 R: all real numbers Continuous

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Chapter 4.5 Graphs of Tangent, Cotangent, Secant, and Cosecant

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  1. Chapter 4.5Graphs of Tangent, Cotangent, Secant, and Cosecant Learning Target:I can generate the graphs for tangent, cotangent, secant, and cosecant.

  2. Tangent Function • f(x) = tan (x) • D: all real numbers except odd multiples of П/2 • R: all real numbers • Continuous • Increasing on each interval in the domain • Symmetric with respect to the origin (odd) • Not Bounded • No extrema • No horizontal asymptotes • Vertical asymptotes: x = k•(П/2) for all odd integers k • End behavior DNE (hence no horizontal asymptotes)

  3. Take a look at the graph of tangent. Why do the vertical asymptotes occur where they do?

  4. Take a look at the graph of cotangent. Why do the vertical asymptotes occur where they do?

  5. Take a look at the graph of Secant. Why do the vertical asymptotes occur where they do?

  6. Take a look at the graph of Cosecant. Why do the vertical asymptotes occur where they do?

  7. Homework Pg. 401 # 3 – 39 every 3rd

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