SOLUTION: Determine the smallest zero for y = 4 sin 3x + 2 in the interval 2pi < x < 3pi I have tried and tried to work this out using trigonometric identities, but I'm just stuck on this

Question 902193: Determine the smallest zero for y = 4 sin 3x + 2 in the interval 2pi < x < 3pi
I have tried and tried to work this out using trigonometric identities, but I'm just stuck on this one question. I am studying for an exam, so I am using this practice exam http://www.bced.gov.bc.ca/exams/specs/resource_exams/precalc12/2013precalc_a_bk1.pdf. It is question 1.
Please show work and explain :)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Determine the smallest zero for y = 4 sin 3x + 2 in the interval 2pi < x < 3pi
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Solve 4sin(3x) + 2 = 0
sin(3x) = -1/2
The smallest positive angle where this is true is in the 3rd Quadrant::
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3x = (7/6)pi
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x = (7/18)pi
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Ans:: The smallest dog in the interval (2pi,3pi)
is 2pi+(7/18)pi = (2+7/18)pi = (43/18)pi
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Cheers,
Stan H.
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