Solultion with Excel Explorations

In the Excel spreadsheet I have put the measure of the base angle (in radians) in Column A and the Area = 2 sin x - .5 sin 2x  in Column B. The value of   a  is set at 1.

 

For the first, I took increments of  .1  with range from  1 radian to  3 radians.   It appears from the graph that the area reach a maximum of a little over 2.

The range where the area is above 2 is for the radian measures of 1.6 to 2.2.   

So a next step would be to look at the graph in a restriced range with finer increments.

 

 

 

 

 

 

 

So, in the next exploration we have shown the range from 1.8 to 2.07. the increments in the radian measures were .01. 

Inspection of the graph and Column B shows the maximum is occuring between 1.94 radians and 1.96 radians.

 

 

 

 

 

 

 

 

 

 

 

 

In the next step the range is shown from 1.93 radians to 1.957 radians with increments of .001

 

Inspection coveys the information that the maximum area is between 2.2018 and 2.019 and the maximum occurs when the base angle is between 1.945 radians and 1.946 radians

 

 

 

 

 

 

 

 

 

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