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Graphs Cosecant Section 4.6

Graphs Cosecant Section 4.6. Objectives. Graph cosecant functions Know key characteristics of the cosecant function. Section 4.5: Figure 4.49, Key Points in the Sine and Cosine Curves. Cosecant Function. We know that cosecant is the reciprocal of Sine Period: 2 

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Graphs Cosecant Section 4.6

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  1. Graphs CosecantSection 4.6

  2. Objectives • Graph cosecant functions • Know key characteristics of the cosecant function

  3. Section 4.5: Figure 4.49, Key Points in the Sine and Cosine Curves

  4. Cosecant Function • We know that cosecant is the reciprocal of Sine • Period: 2 • Since csc = 1/sin; we know that cosecant does not exist when sin x = 0 (zero would be in denominator) • When is sin x = 0? • 0 and  • These will be Vertical Asymptotes

  5. To graph y = csc x, use the identity . y Properties of y = csc x 1. domain : all real x x 4. vertical asymptotes: Graph of the Cosecant Function Cosecant Function At values of x for which sin x = 0, the cosecant functionis undefined and its graph has vertical asymptotes. 2. range: (–,–1]  [1, +) 3. period: 2 where sine is zero.

  6. y y 2 2 x x ˝ -˝ ˝ -2 -2 Text Example Use the graph of y = 2 sin 2x to obtain the graph of y = 2 csc 2x. Solution The x-intercepts of y = 2 sin 2x correspond to the vertical asymptotes of y = 2 csc 2x. Thus, we draw vertical asymptotes through the x-intercepts. Using the asymptotes as guides, we sketch the graph of y = 2 csc 2x.

  7. Homework • Worksheet 9-5

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