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Chapter 6: Q. 23 (page 429)

In Problems 19鈥�26, apply the methods of this and the previous section to graph each function. Be sure to label key points and show at least two periods.

y=-cot(2x+蟺2)

Short Answer

Expert verified

The graph of the function y=-cot(2x+蟺2)is:

Step by step solution

01

Step 1. Given

The functiony=-cot(2x+蟺2)

To graph the function with at least two cycles.

02

Step 2. Find the amplitude, period and phase shift.

Compare the given function y=-cot(2(x-(-蟺4)))with y=Asin(蝇x-蠒)+B

No amplitude

Period, 2蟺蝇=蟺2

Phase shift, 蠒蝇=-蟺4

03

Step 3. Determine x-coordinates

One cycle begins at x=蠒蝇(-蟺4)and ends at

x=蠒蝇+2蟺蝇=-蟺4+蟺2=蟺4

To find the five key points, divide the interval (-蟺4,蟺4)into four sub intervals, each of length 蟺2梅4=蟺8

-蟺4+蟺8=-蟺8

-蟺8+蟺8=0

0+蟺8=蟺8

蟺8+蟺8=蟺4

The x-coordinates are -蟺4,-蟺8,0,蟺8,蟺4

04

Step 4. Determine the key points

Use these values of xto determine the key points on the graph:

The key points include (-蟺8,-1),(0,0),(-3蟺8,1),(蟺8,1),(3蟺8,-1)

05

Step 5. Sketch the graph

Plot these five points and fill in the graph of the function.

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