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Find All Solutions to the Equation cosx=12\cos x = - \frac { 1 } { 2 }

Question 275

Multiple Choice

Find all solutions to the equation.
- cosx=12\cos x = - \frac { 1 } { 2 } (Express your answer in radians, in exact form.)


A) {5π6+nπn=0,±1,±2,.}\left\{ \frac { 5 \pi } { 6 } + \mathrm { n } \pi \quad \mathrm { |n } = 0 , \pm 1 , \pm 2 , \ldots . \cdot \right\}
B) {2π3+2nπ,4π3+2nπn=0,±1,±2,}\left\{ \frac { 2 \pi } { 3 } + 2 \mathrm { n } \pi , \frac { 4 \pi } { 3 } + 2 \mathrm { n } \pi \mid \mathrm { n } = 0 , \pm 1 , \pm 2 , \ldots \right\}
C) {2π3+nπn=0,±1,±2,}\left\{ \frac { 2 \pi } { 3 } + n \pi \quad \mid \mathrm { n } = 0 , \pm 1 , \pm 2 , \ldots \right\}
D) {5π6+2nπ,7π6+2nπn=0,±1,±2,}\left\{ \frac { 5 \pi } { 6 } + 2 \mathrm { n } \pi , \frac { 7 \pi } { 6 } + 2 \mathrm { n } \pi \mid \mathrm { n } = 0 , \pm 1 , \pm 2 , \ldots \right\}

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