Find the exact value of sin(−712)
sin(-7pi/12)
= -sin(7pi/12)
= -sin(pi/4 +pi/3)
= -[sin(pi/4)cos(pi/3) +cos(pi/4)sin(pi/3)]
= -[(1/sqrt(2))(1/2) +(1/sqrt(2))(sqrt(3)/2)]
= -[1 /2sqrt(2) +sqrt(3) /2sqrt(2)]
= -(sqrt(2) /4)(1 +sqrt(3)) -----answer.
or,
= -(1/4)[sqrt(2) +sqrt(6)] ---------answer also