emilyr123
4sin(theta)+3sqrt3=sqrt3
solve w/ interval 0 < theta < 2pi



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psi9epsilon
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Pretty straightforward
\[4 \sin (\theta) = \sqrt{3}  3\sqrt{3}\]

psi9epsilon
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\[4\sin (\theta)=2\sqrt{3}\]

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\[\sin (\theta)=2\sqrt{3 } / 4\]

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\[\sin (\theta)=\sqrt{3} / 2\]

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\[\theta = \sin^{1} (\sqrt{3}/2)\]

psi9epsilon
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sin THETA is NEGATIVE only in 3rd and 4th quadrant

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\[\theta=\sin^{1} (\sin(\pi+\pi/3))\]

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THETA = 4 PI /3

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OR THETA = 2PI  PI/3 = 5PI/3

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TWO ANSWERS as the interval is from 0 > 2 Pi