aSin(x) + bcos(x)

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This group of interactive excel worksheets look at the series of identities of the form

aSin(x) ± bCos(x) and aCos(x) ± bSin(x),

where a=RCos(α), b = RSin(α), R=√(a2+b2) and α=tan-1(b/a).

The first sheet contains the basic four formulae which can be revealed a line at a time.

The second sheet illustrates aSin(x) + bCos(x) by plotting aSin(x), bCos(x) and their sum. The values of a and b can be adjusted in order to see the changes this has on the three curves. The value for R and α are also calculated.

The following three sheets repeat this process for aSin(x) - bCos(x), aCos(x) - bSin(x) and aCos(x) + bSin(x).

The final section contains a set of 6 functions from which students can find the maximum and minimum values and the value of x at which they occur. The graph for each function can be displayed by clicking on the “Graph” button.

Note
This program was designed by be viewed on a screen with a resolution of 1024 x 768. Users may have to adjust the resolution of their screen for the pages to display as was originally intended. The program uses macros which need to be enabled on users’ machine.

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