Question

sin(-x)=-sin x for all values of x
true or false.

Answer 1

Proving identities often involves turning one side into another using some known identities.
Perhaps use the fact that
\[\Large -x = 0-x\]
and
\[\Large \sin(a - b) = \sin(a)\cos(b)-\cos(a)\sin(b)\]

Answer 2

Not to mention
\[\large \sin(0)=0\\\large \cos(0)=1\]

Answer 3

so its true

Answer 4

Find out.
As per those identities, what is
\[\Large \sin(-x) = \sin(0-x)=\color{red}?\]

Answer 5

true

Answer 6

sources : http://www.wolframalpha.com/input/?i=sin%28-x%29%3Dsin%280-x%29

Answer 7

Thanks :)

Answer 8

I'm certain you're not allowed to use that resource :3
Come on...
\[\Large \sin(\color{red}a-\color{blue}b) = \sin(\color{red}a)\cos(\color{blue}b) - \cos(\color{red}a)\sin(\color{blue}b)\\\Large \sin(\color{red}0-\color{blue}x) = \sin(\color{red}0)\cos(\color{blue}x) - \cos(\color{red}0)\sin(\color{blue}x)\]

Answer 9

and knowing that sin(0) = 0
and cos(0) = 1
you get the identity you need.

Answer 10

Yes it is true for all values of x.