# Thread: Graphing trig expressions such as sin(1/x)

1. ## Graphing trig expressions such as sin(1/x)

Hello,

How would I go about sketching for example the graph of sin(1/x) (without using software). What though process should I go through? I am thinking about drawing the graph of sin(x) and trying to think about what happens when x increases?

Many thanks for any help,
Aaron.

2. Not bad, but you must pay careful attention.

1) y = sin(x) is wonderfully periodic and you will not ever find anything interesting, unless
2) You figure out that your transformation x ==> 1/x is NOT linear.
2a) [1,10] ==> [1,0.1]
2b) [10,100] ==> [0.1,0.01]
2c) [100,1000] ==> [0.01,0.001]

For 2a, we mapped 9 greater than 1 onto 0.9 less than 1. That's quite a bit of compression.
For 2b, we mapped 90 greater than 10 onto 0.09 less than 0.1. That's a whole bunch of compression.
For 2c, ... are you seeing it, yet?

3. Ok, I can see that because the 1/x part is not linear, as it gets closer to x = 0 (which is not defined) it compresses until it gets to that undefined value. How would I determine what the graph looks like when the x values get large? I suppose 1/x gets very small, does the curve continue oscillating or does it converge?