Question 979237


{{{3*sin(pi*X)}}} + {{{3*sqrt3*cos(pi*X)}}} = {{{3*2}}}.{{{((1/2)*sin(pi*X) + (sqrt(3)/2)*cos(pi*X))}}} = {{{6}}}.{{{(sin(pi/6)*sin(pi*X) + cos(pi/6)*cos(pi*X))}}} = {{{6}}}.{{{sin(pi/6 + pi*X)}}} = {{{6}}}.{{{sin(pi*(1/6 + X))}}}. 


We used here the addition formula for sines 


{{{sin(alpha + beta)}}} = {{{sin(alpha)*sin(beta) + cos(alpha)*cos(beta)}}}


of &nbsp;<B>Trigonometry</B>&nbsp; (see, &nbsp;for example, &nbsp;the lesson &nbsp;<A HREF=http://www.algebra.com/algebra/homework/Trigonometry-basics/Addition-and-subtraction-formulas.lesson>Addition and subtraction formulas</A>&nbsp; in this site), &nbsp;and the facts that


{{{cos(pi/6)}}} = cos(30°) = {{{sqrt(3)/2}}} &nbsp;&nbsp;and&nbsp;&nbsp; {{{sin(pi/6)}}} = sin(30°) = {{{1/2}}}.