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Answer 1 · 2017-12-01T13:34:55

The solutions are #S={41.8^@, 138.2^@}#

The equation is #3sin^2x-11sinx+6=0#

This isa quadratic equation in #sinx#

The discriminant is

#Delta=b^2-4ac=(-11)^2-4*(3)*(6)=121-72=49#

As #Delta>0#, there are #2# real roots

#sinx=(11+-sqrt49)/(2*3)=(11+-7)/(6)#

So,

#sinx=3# or #sinx=4/6=2/3#

Therefore,

#3sin^2x-11sinx+6=(3sinx-2)(sinx-3)#

The solutions are

#sinx=3#, #=>#, #x=O/#

and

#sinx=2/3#, #=>#, #x=41.8^@#and #x=138.2^@# , for #x in [0,pi]#