how to sketch a graph of the product of two trig identities?

Hey all,

so, I have encountered a problem that asks me to sketch the graph of the following: f(x) = sin(x)cos(12x). I know how to sketch them both separately, but what is the procedure so that I can do this properly without using a calculator?

another type of problem asks me to sketch something like this: 4cos(x)-3sin(x). I have the same issue here as I would the above example.

thanks in advance for your help!

Re: how to sketch a graph of the product of two trig identities?

Test the f(x) values incrementally, to get a rough idea on the structure of the graph.

If this is between [0, ], test:

0, , , , , , , , .

Given that the frequency of the cosine function is 12, you may want to do , , etc as well..

Essentially, do what you did in high school when you first learnt how to graph linear equations, have a row of values for x, and a row for f(x).

Of course, there is always Wolfram|Alpha; it can give you some guidance.

sin(x)cos(12x) - Wolfram|Alpha

Re: how to sketch a graph of the product of two trig identities?

Additionally, you might make use of trig identities, when convenient.

Your second example, for example, can be written in the form

The first one can be written in the form

which doesn't help quite so much.