Anyone know of any good resources for learning how to better sketch trig functions? I have not had to fool much with trig since before my freshman year so I am kinda rusty on this.

For example, how would I go about sketching the following:
y = (e^-t) * (2cos(7t) + 3sin(7t))

Given that the first term is e^-t, I know that as t gets bigger that the function will get closer and closer to zero (and conversely that as t gets smaller y will explode to infinity). However, I am not sure how to think about skeching the second term.

If I was just sketching 3sin(7t) I know the amplitude would be 3 and the period of the function would be reduced by 1/7 from the original. So the peaks would be higher and closer to each other than in a normal sin function. Right?

Where I am having trouble is adding the cos function on top of that and then multiplying it all by the exponential function. Any links or helpful advice would be great. Thanks a lot!!

2/7/2010 3:29:10 PM

the fact that it's trig isn't really consequential--it's just a composition of functions question

cos is just sin shifted by pi/2 in time

2/7/2010 8:19:27 PM

2/8/2010 8:25:39 AM

^hahaha

2/8/2010 11:37:22 AM

Why sketch when you can Matlab:

t = linspace(-2*pi, 2*pi, 1000);
y = exp(-t) .* (2 .* cos(7 .* t) + 3 .* sin(7 .* t));
plot(t,y)

2/8/2010 3:38:32 PM

a monkey can use software to graph.

only someone who truly understands and appreciates math intuitively can sketch them.

2/8/2010 6:05:27 PM

^ or you could just feed fractions of pi into the formula until you can fill in the "picture"

2/8/2010 6:09:27 PM

http://fooplot.com/e^(-x)*(2cos(7x)+3sin(7x))

2/9/2010 2:04:42 PM