What are the solutions to sinx= -root3/2
sin is a repeating function, [ so sin60 = sin(p - 60) = sin(2p + 60) = sin(3p - 60) = sin(4p + 60) = ... or more generally sinx = sin(2pn + x) = sin(2pn + p - x) soooo.... inverse sin(-v3/2) = -p/3 for all the values of sin(2pn + x)... -6p + (-p/3) ; -4p + (-p/3) ; -2p + (-p/3) ; 0p + (-p/3) ; 2p + (-p/3) ; 4p + (-p/3) ; 6p + (-p/3) -(19/3)p ; -(15/3)p ; -(7/3)p ; -p/3 ; (5/3)p ; (11/3)p ; (17/3)p for all the values of sin(2pn + p - x)... -6p + p - (-p/3) ; -4p + p - (-p/3) ; -2p + p - (-p/3) ; 0p + p - (-p/3) ; 2p + p - (-p/3) ; 4p + p - (-p/3) ; 6p + p - (-p/3) -(14/3)p ; -(8/3)p ;
-(2/3)p ; (4/3)p ; (10/3)p ; (16/3)p ; (22/3)p Possible values for x are -(19/3)p ; -(15/3)p ; -(14/3)p ; -(8/3)p ; -(7/3)p ; -(2/3)p ; -p/3 ; (4/3)p ; (5/3)p ; (10/3)p ; (11/3)p ; (16/3)p ; (17/3)p ; (22/3)p Now strip out the ones that aren't in the range -3p and +3p... Possible values for x are -(8/3)p ; -(7/3)p ; -(2/3)p ; -p/3 ; (4/3)p ; (5/3)p ]
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