Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

THETA = 4 PI /3

Answer 9

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

Answer 10

TWO ANSWERS as the interval is from 0 -> 2 Pi