In Exercises 45–52, graph two periods of each function. y = cs...

Question

In Exercises 45–52, graph two periods of each function. y = csc|x|

Accepted Answer

Sketch the graph of the following sequent function using the two periods Y equals two cos of the absolute value of two X. No. We have a graph here. We can plot our equation on. And to do this, we first need to see the characteristics of our equation. Let's first write this as a reciprocal function. In terms of time, you have two sine absolute value two X co sequent will have the same characteristics. So we can use this sine function to find this period as well as amplitude and phase shift. So a science functions basic formula is a stein BX minus C plus D where A is the amplitude, our period is given by two pi divided by B. Our phase shift is given by C divided by B. And finally, we have vertical shift which is just D. Now we know this, we have a two in front of our son, which is our A, that is our amplitude. Our period will be two pi divided by two, which is pi our phase shift is C divided by B. Now we don't have AC. So this is just a zero same for D. This is also zero. Now it says you want to graph this over two periods. So we will use two periods of our sine function. You will actually go from negative pi to positive type. Now we can go ahead and try and graph our function. The graph codes seeking we first need the graph sign. So we can find some values to plug into this sign function. And we can put on our graph with our output values. For example, this table down here gives us some values between native pi and pi. Our first one for instance is negative pi zero. Then we have negative three pi divided by four, negative two, negative pi divided by 20, negative pi divided by 42 and 00. We do the same in the other direction divided by four or two pi divided by 203 pi divided by four negative two and pi zero. Now we can draw a curve between these points. Since this is absolute value, we will jump and have a little sharp point at the bottom there at zero and keep going. Now this is just the sine function. We wanted to cos it the co sequent we can find from this graph. We first see the draw asym totes everywhere where our sine function is equal to zero. So we have a few ascent to we can draw on here. No, we can draw curves coming from each of our remaining points. For instance at three pi divided by four, we can start the point there at the same place and curved downwards hugging the ATO on the left and to the right will do the same for every other point. We're divided by four. We go up instead and we should get a bunch of curves pointing up or down, separated by asom totes, which that makes our sequent function. OK? I hope to help you solve the problem. Thank you for watching. Goodbye.

In Exercises 45–52, graph two periods of each function. y = csc|x|

Key Concepts

Understanding the Cosecant Function (csc x)

Effect of the Absolute Value on the Input (|x|)

Periodicity and Graphing Multiple Periods

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