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Understanding and Graphing Tan, Cot, Sec, and Csc Functions

Explore the concepts of tangent, cotangent, secant, and cosecant functions in this comprehensive chapter. Learn about the amplitude, period, domain, and range of tangent and cotangent functions, along with their transformations. This guide provides step-by-step instructions for graphing two periods of these functions while identifying key characteristics such as maximum and minimum values. Additionally, delve into the graphing of secant and cosecant functions, including vertical asymptotes and corresponding sine or cosine functions. Enhance your understanding of trigonometric functions through practical examples.

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Understanding and Graphing Tan, Cot, Sec, and Csc Functions

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  1. Chapter 14 Day 9 Graphing Tan, Cot, Sec, Csc

  2. Graphing Tangent tanx

  3. What is the amplitude of the tangent function? • What is the period of the tangent function? • What is the domain of the tangent function? • What is the range of the tangent function?

  4. Graphing Tangent cotx

  5. What is the amplitude of the cotangent function? • What is the period of the cotangent function? • What is the domain of the cotangent function? • What is the range of the cotangent function?

  6. Transformations of Tan and Cot Graphs • Follow the same rules as for sin and cos when shifting up or down. • Since the period of the tan and cot function is to find the period when changed: • The amplitude of tangent: π

  7. Graph two periods of the function. State the amplitude, period, maximum, and minimum. 1.

  8. Graph two periods of the function. State the amplitude, period, maximum, and minimum. 2.

  9. Graph two periods of the function. State the amplitude, period, maximum, and minimum. 3.

  10. Graph two periods of the function. State the amplitude, period, maximum, and minimum. 4.

  11. Graphing Secant and Cosecant • 1. Graph the corresponding sine or cosine function with the given transformation. • 2. Draw in vertical asymptotes where the sine or cosine function crosses the midline. • 3. Draw in the secant or cosecant function. • 4. The period of the secant and cosecant functions is . • 5. The amplitude of the secant and cosecant function is .

  12. Graph one period of the function. State the amplitude, period, maximum, and minimum. 5.

  13. Graph one period of the function. State the amplitude, period, maximum, and minimum. 6.

  14. Graph one period of the function. State the amplitude, period, maximum, and minimum. 7.

  15. Graph one period of the function. State the amplitude, period, maximum, and minimum. 8.

  16. Graph one period of the function. State the amplitude, period, maximum, and minimum. 9.

  17. Graph one period of the function. State the amplitude, period, maximum, and minimum. 10.

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