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Find All Solutions to the Equation sinx=32\sin x = \frac { \sqrt { 3 } } { 2 } \quad

Question 260

Multiple Choice

Find all solutions to the equation.
- sinx=32\sin x = \frac { \sqrt { 3 } } { 2 } \quad (Express your answer in radians, in exact form.)


A) {π3+2nπ,5π3+2nπn=0,±1,±2,}\left\{ \frac { \pi } { 3 } + 2 \mathrm { n } \pi , \frac { 5 \pi } { 3 } + 2 \mathrm { n } \pi \mid \mathrm { n } = 0 , \pm 1 , \pm 2 , \ldots \right\}
B) {π3+nπn=0,±1,±2,}\left\{ \frac { \pi } { 3 } + n \pi \quad \mathrm { n } = 0 , \pm 1 , \pm 2 , \ldots \right\}
C) {π6+2nπ,5π6+2nπn=0,±1,±2,}\left\{ \frac { \pi } { 6 } + 2 \mathrm { n } \pi , \frac { 5 \pi } { 6 } + 2 \mathrm { n } \pi \mid \mathrm { n } = 0 , \pm 1 , \pm 2 , \ldots \right\}
D) {π3+2nπ,2π3+2nπn=0,±1,±2,}\left\{ \frac { \pi } { 3 } + 2 \mathrm { n } \pi , \frac { 2 \pi } { 3 } + 2 \mathrm { n } \pi \mid \mathrm { n } = 0 , \pm 1 , \pm 2 , \ldots \right\}

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