Question 979784


Hello,


I read your writing   sin(tan^-1(-1)+sin^-1(1/2))   as


{{{sin(arctan(-1) + arcsin(1/2))}}}.


Do I read correctly?


If my reading is correct,  then the rest part is simple.


{{{arcsin(1/2)}}} = {{{pi/6}}} = 30°,


{{{arctan(-1)}}} = {{{-pi/4}}} = -45°.


sin(30° -  45°) = sin(30°)*cos(45°) - cos(30°)*sin(45°) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(subtraction formula for sines of &nbsp;<B>Trigonometry</B>, &nbsp;see 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;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= {{{1/2}}}.{{{sqrt(2)/2}}} - {{{sqrt(3)/2}}}.{{{sqrt(2)/2}}} = {{{sqrt(2)/4}}} - {{{sqrt(6)/4}}} = {{{(sqrt(2)-sqrt(6))/4}}} = {{{-(sqrt(6)-sqrt(2))/4}}} = -0.259.