provide counter example

[TrueTears]

For the function with the rule f(x)=sin(x), give a counter example to show that f(x+y) does not equal f(x)+f(y) for all x and y.

Is there a systematic way to approach this? or is it just guess what, ie plugging in values until u find one which doesn't work?

[Collin Li]

Now, does for all values of and ?

Probably not. Just pick some values for and to show this is not true (i.e.: a counter-example).

Hint, choose to be an angle with an associated exact value, i.e.:



This is probably the best way to approach it.

[TrueTears]

awesome thanks coblin!