Sketching Trigonometric Curves: Tips and Tricks

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To sketch the curve y = sin(4x)cos(x) over the interval [0, pi/2], it's helpful to first graph y = sin(4x) and y = cos(x) separately. The graph of y = sin(4x) resembles y = sin(x) but does not extend below the x-axis. The product of these two functions, y = sin(4x)cos(x), will be zero wherever either function is zero. Using this method provides a clear visual representation of the combined behavior of the functions. Understanding the individual components simplifies the sketching process for complex trigonometric curves.
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Homework Statement



I need to sketch this curve from [0, pi/2]

y = sin4xcosx

Homework Equations


The Attempt at a Solution



I tried to generate this thing on a graphing program to see how it looked like.. otherwise I would have no idea what this is.

Is there some easy tips to use to sketch these weird curves? Like by the derivative or something funky?
 
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Sketch y = sinx.
Sketch y = sin4x. It's graph will be similar to the graph of y = sinx, except that no part of the graph of y = sin4x extends below the x-axis.

On the same graph as y = sin4x, graph y = cosx. The graph of y = sin4x*cosx will be the product of the two functions. Where one function's value is zero, the product of the two will be zero. Doing this, you should get a reasonably accurate graph.
 

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