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anonymous
 one year ago
Why does
Sin[x c]
Simplify to
Sin[cx] ?
I mean what would be the reason to not just leave it as xc ?
anonymous
 one year ago
Why does Sin[x c] Simplify to Sin[cx] ? I mean what would be the reason to not just leave it as xc ?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0First sin function is an odd, so f(x) = f(x)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and you ca use trig identities to prove that also

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.0well.. or one could use the "symmetry identities" and notice that sin(a) = sin(a) thus sin([xc]) is also equals to sin( [c x]) which also would equal sin([cx]) or just sin(cx)

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.0you could expand it if you wish anyhow, using the sum identity, and you'd end up with sin(x+c) keeping in mind that x+c is also equals to (cx) < expand that and you'd get x+c

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.0x+c would equal (cx) < expanding that would give x+c

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thanks guys.. now I understand the conversion process a bit better. I'm still a bit curious when mathematica is asked to simplify sin[xc] why it chooses the sin[cx] form as the preferred form, this doesn't seem simplified to me. Is there a general rule that gives one form priority over the other?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It depends on what will you do with that expression or neighborhood expressions to make them look identical and factor out or something like that. anyway this example "for me" is meaningless as itself and the word simplify is ambiguous. So i would go with making it sin x cos c cos x sin c

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It's because it is easier to understand \(\sin(xc)\) as a function that is shifted and then reflected.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Basically, \(\sin(x)\) is generally easier to evaluate than \(\sin(x)\) because the table of \(\sin(x)\) values likely did not have negative \(x\) values as it would be redundant.
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