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Chapter 6: Q. 20 (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=12cot(2x-蟺)

Short Answer

Expert verified

The graph of the function y=12cot(2x-蟺)is:

Step by step solution

01

Step 1. Given

The functiony=12cot(2x-蟺)

To graph the function with at least two cycles.

02

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

Compare the given function y=12cot(2(x-蟺2))with y=Asin(蝇x-蠒)+B

No Amplitude

Period, T=2蟺蝇

=蟺2

Phase shift, 蠒蝇=蟺2

03

Step 3. Determine x-coordinates

The graph of y=12cot(2(x-蟺2))

One cycle begins at x=蠒蝇(蟺2)and ends at x=蠒蝇+2蟺蝇

=蟺2+蟺2=蟺

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

蟺2+蟺8=5蟺8

5蟺8+蟺8=3蟺4

3蟺4+蟺8=7蟺8

7蟺8+蟺8=蟺

The x-coordinates are 蟺2,5蟺8,3蟺4,7蟺8,蟺

04

Step 4. Determine the key points.

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

The key points include (5蟺4,0),(3蟺4,0),(7蟺8,-12),(蟺8,12),(蟺4,0)

05

Step 5. Sketch the graph.

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

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