6cos 289sin 90 Solution6cos29sin90 61sin2 9sin90 66sin2 9sin

Solution

6cos²-9sin-9=0

=>6(1-sin²) -9sin-9=0

=>6-6sin² -9sin-9=0

=>-6sin² -9sin-3=0

=>-3(2sin² +3sin+1)=0

=>2sin² +3sin+1=0

=>2sin² +3sin=-1

=>sin² +(3_/2)sin=-(1_/2)

=>sin² +(3_/2)sin+(3_/4)²=(3_/4)²-(1_/2)

=>(sin +(3_/4))²=(9_/16)-(1_/2)

=>(sin +(3_/4))²=(1_/16)

=>(sin +(3_/4))=-(1_/4),(sin +(3_/4))=(1_/4)

=>sin =-(3_/4)-(1_/4),sin =-(3_/4)+(1_/4)

=>sin =-1,sin =-(1_/2)

general solution: = 2n -(_/2) ,2n -(_/6),2n-(5_/6) , where n is an integer

in interval [0,2) , =7_/6,3_/2, 11_/6