## Function

f(x,y) = p sin(qy)

## Domain

xandyare elements of the set of allReal numbers

## Graphs

## Derivative

With respect tox:0

With respect toy:p cos(qy)qCritical points are formed where the two derivatives equal 0. These critical points may be minimums, maximums, or saddle points. In the first graph, for

y, 0 =cos(y)which happens atn*Pi/2, for alln. Forx, 0 = 0 for allxvalues. From the graph, it shows that the lines fory = n*Pi/2are the ridges that run high and low.

## Integral

With respect tox:p sin(qy)x

With respect toy:(-cos(qy)p)/q

## Interesting Features

When working with this function, there are many different items to look at. The

pscales the values up and down. If it is left out, the graph goes from -1 to 1. The graph goes from-ptop. This is shown in the graph of 2sin(y). Theqvalue scales the angle. If it is left out, the values remain the same as the angle. This means that the graph completes one cycle in 2*Pi radians. The graph ofsin (2y)shows this when the angles are doubled, the graph completes one cycle in only Pi radians.

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