# Question: An appropriate window setting for the graph of `y=(20.1sin)(2pi)/(300)(t-265)+6.2` is A. x:[0, 17000, 5000], y:[-20, 30, 10] B. x:[-265, 0, 50], y:[0, 12.4, 1] C. x:[0, ` `600, ` `100],...

Question: An appropriate window setting for the graph of `y=(20.1sin)(2pi)/(300)(t-265)+6.2` is

A. x:[0, 17000, 5000], y:[-20, 30, 10]

B. x:[-265, 0, 50], y:[0, 12.4, 1]

C. x:[0, ` `600, ` `100], y:[-15, 30, 5] ANSWER

D. x:[0, `2pi` , `Pi/2` ], y:[-20, 30, 5]

This is the answer, Please somebody can explainme more with details!(I did not understand why use minimum and maximum)

From the equation, determine the min/max positions, and the length of a cycle.

`y=(20.1sin)(2pi)/(300)(t-265)+6.2`

`b=(2pi)/(period)=(2pi)/(300)` `~~period=300`

Minimum: 6.2-20.1=-13.9

Maximum: 6.2+20.1=26.3

A window setting that allows us to see all these points is

C. x:[0, ` `600, ` `100], y:[-15, 30, 5] ANSWER

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### 1 Answer

Given `y=20.1sin((2pi)/300(t-265))+6.2`

The midline is 6.2.

The amplitude is 20.1 so the maximum and minimum are 26.3 and -13.9 repectively.

The period can be found by `p=(2pi)/(((2pi)/300))=300` .

There is a phase shift (horizontal translation) of 265 units to the right.

In order to see the graph, we would like to see 1 complete period (at least); we want to see the maximum and minimum and the zeros.

To see 1 complete period the x-values must be separated by at least 300 units. (A) gives 17000 units, but this shows over 50 sine waves -- it is difficult to see the interesting features. (B) does not give a complete period. (C) gives 2 periods, 1 complete period from 0 to max to 0 to min and back to max. (D) uses the wrong units for x.

To see the maximum and minimum we need to set y so that it includes -13.9 and 26.3. (A) would work, (B) shows neither maximum nor minimum, (C) gives the full range without a lot of extra as does (D).

You will want to play with these. In future courses it is important to be able to recognize when a different window is called for. You will need to learn what the interesting features of different types of graphs are.

Here are the graphs so you can compare:

(A)

This graph does not even show the correct number of periods. Most graphing utilities will exhibit some sort of bad behavior when asked to show too much.

(B)

(C)

(D)

When I graphed in a TI-83 I used x: -50,300,15 and y: -15,30,5 to get