#sin^-1(0.66) = 0.0065w#
Be sure to set your calculator in "Rad" (radian) mode
#0.0065w =sin^-1(0.66) = .720819#
#w =.720819/.0065 = 110.8952...= 110.9 #
If you don't get the answer above, your calculator is probably not set in the radian mode.
Actually for # sintheta=a #, the general solution is:
#sintheta, sin(pi-theta), sin(2pi+theta),sin(3pi-theta), sin(4pi+theta)+...= a#
#rArr sin(npi+(-1)^ntheta)= a " for " n=0, 1, 2.."integer".#
#rArr npi+(-1)^ntheta= sin^-1a #
#theta = ( sin^-1a- npi)/(-1)^n = (-1)^n (sin^-1a- npi)#
with #n =0, 1, 2, 3, .. "integer".#*
Substitute # a =.66 and theta=0.0065w and solve " for " w#
#w =((-1)^n (.720819-npi))/.0065#
#w= 110.9, 372.43, 1339.07, ... for n=0, 1, 2, .."integer"#
*Note: #(-1)^n = (-1)^-n if n =0, 1, 2.. "integer"#
