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Chapter 7: Trigonometric Graphs 7.2: Graphs of the Cosecant, Secant, and Cotangent Functions

Chapter 7: Trigonometric Graphs 7.2: Graphs of the Cosecant, Secant, and Cotangent Functions. Essential Question: How do the graphs of csc, sec and cot relate to their inverse functions?. 7-2: Graphs of Csc/Sec/Cot. The Cosecant Function

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Chapter 7: Trigonometric Graphs 7.2: Graphs of the Cosecant, Secant, and Cotangent Functions

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  1. Chapter 7: Trigonometric Graphs7.2: Graphs of the Cosecant, Secant, and Cotangent Functions Essential Question: How do the graphs of csc, sec and cot relate to their inverse functions?

  2. 7-2: Graphs of Csc/Sec/Cot • The Cosecant Function • Because sin t and csc t are reciprocals, the curves meet at the same peaks, they just go in opposite directions. • The graph of csc t is undefined wherever sin t would equal 0 • Red = sin t • Blue = csc t

  3. 7-2: Graphs of Csc/Sec/Cot • The Secant Function • The sec/cos graphs behave just like the csc/sin graphs. • The graph of sec t is undefined wherever cos t would equal 0 • Red = cos t • Blue = sec t

  4. 7-2: Graphs of Csc/Sec/Cot • The Cotangent Function • Looks just like the tangent function, only flipped horizontally. Why? • The graph of cot t is undefined wherever tan t would equal 0, meaning its undefinedat each interval of π • Red = tan t • Blue = cot t

  5. 7-2: Graphs of Csc/Sec/Cot • Reflection and Vertical Stretches • Graph -3 csc t • Use the reciprocal graph: -3 sin t • Take that graph, and flip the curves • Red = -3 sin t • Blue = -3 csc t

  6. 7-2: Graphs of Csc/Sec/Cot • Vertical Stretch and Vertical Shift • Graph 2 sec t – 3 • Use the reciprocal graph: 2 cos t – 3 • Take that graph, and flip the curves • Red = 2 cos t – 3 • Blue = 2 sec t – 3

  7. 7-2: Graphs of Csc/Sec/Cot • Reflection, Vertical Stretch, and Horizontal Shift • Graph -3 cot(t – π/4) • Take the parent function: cot t, which is the reciprocal of tan t • Shift it π/4 units to the right • Flip it vertically • Stretch it by a factor of 3 tan t cot t cot(t – π/4) -cot(t – π/4) -3cot(t – π/4)

  8. 7-2: Graphs of Csc/Sec/Cot • Assignment • Page 490 – 491 • Problems 1 – 17, odd

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