Question 69605
<font size = 5><pre><b>I am trying to use the addition and subtraction 
formulas to simplify

{{{ sin(2pi- x) }}}. 


I am not sure where to begin.

You have to know the formula

{{{ sin(A-B) = sin(A)cos(B)-cos(A)sin(B)}}}

Substitute {{{2pi}}} for A and {{{x}}} for B

{{{ sin(2pi-x) = sin(2pi)cos(x)-cos(2pi)sin(x)}}}

Now use the fact that 

{{{sin(2pi) = 0}}} and {{{cos(2pi) = 1}}}

Substituting those:

{{{ sin(2pi-x) = (0)cos(x)-(1)sin(x)}}}

{{{(0)cos(x)}}} is just 0 and we can erase the 1:

{{{ sin(2pi-x) = -sin(x)}}}

Edwin</pre>