2. Graphs Cosecant Section 4.6

3. Objectives Graph cosecant functions Know key characteristics of the cosecant function

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

5. 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

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

7. 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. y -2 2 x ˝-˝ y -2 2 x ˝ Text Example

8. Homework Worksheet 7-5