Question 417424
{{{sin(3/4)*pi = 135}}} degrees


{{{135}}} deg. lies in the {{{2nd}}} quadrant


little more:


It is the {{{same}}} as {{{45 deg}}}, but a reference angle.


{{{sin(45)= leg/hyp = 1/sqrt(2)= sqrt(2)/2}}}


{{{cos(45)=1/sqrt(2)= sqrt(2)/2}}}


But in the second quadrant {{{highlight(sine)}}}is{{{positive}}} and {{{highlight(cosine)}}} is {{{negative}}}





so, {{{sin(3* pi/4) = 1/sqrt(2)=sqrt(2)/2}}}

{{{cos(3 *pi /4) = -1/sqrt(2)=-sqrt(2)/2}}}}



This will summarizes all:

Quadrant I: 0 to 90 degrees = 0 to p/2 radians

Quadrant II: 90 to 180 degrees = p/2 to p radians

Quadrant III: 180 to 270 degrees = p to 3p/2 radians

Quadrant IV: 270 to 360 degrees = 3p/2 to 2p radians

where p = 3.14 rounded to 2 decimal places.