Question 1079851
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<pre>
The angle {{{(-21pi)/4}}} is geometrically equivalent to {{{(-21pi)/4 + 2pi}}} = {{{(-21pi + 8pi)/4}}} = {{{-13pi/4}}},


which, in turn, is geometrically equivalent to

{{{-13pi/4+2pi}}} = {{{(-13pi+8pi)/4}}} = {{{-5pi/4}}},


which, in turn, is simply the same as {{{3pi/4}}}.


The function sine is periodical with the period of {{{2pi}}}, therefore,


{{{sin((-21pi)/4))}}} = {{{sin((-13pi)/4)}}} = {{{sin((-5pi)/4))}}} = {{{sin(3pi/4)}}} = {{{sqrt(2)/2}}}.
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Solved.