Please help! I keep getting this problem wrong. Use trigonometric identities to

Question

Please help! I keep getting this problem wrong. Use trigonometric identities to solve the equation in the interval [0,2pi) Ma ork: Section 6-5 Homework : O of 1 pt HW 66.67% (6 of 9 pts) Use trigonometric identities to so tion m 6cos 20 + 9 sin -9:0 Select the correct choice and fillin any answer boxes in your choice below (Type your ansd in radians. Type an exact answer, using as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed) OB. There is no solution. Clear All drawing

Explanation / Answer

6cos2+ 9 sin - 9 = 0

write cos2=1-sin2

6(1-sin2)+ 9 sin - 9 = 0

3(2(1-sin2)+ 3 sin - 3) = 0

2(1-sin2)+ 3 sin - 3 = 0

2-2sin2+ 3 sin - 3 = 0

2sin2- 3 sin +1=0

2sin2- 2sin -sin +1=0

2sin (sin -1)-1(sin -1)=0

(sin -1)(2sin -1)=0

sin -1 =0 ,2sin -1=0

sin =1 ,sin =1/2

sin =1 => =/2

sin =1/2 => =/6 ,5/6

=/6 ,/2,5/6

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