Himpunan penyelesaian persamaan sin 2x-1/2 akar 3=0 untuk 0<_x<_3phi/2 adalah

<p>Jawabannya adalah &nbsp;{π/6, &nbsp;π/3, 7π/6, 4π/3}</p><p>&nbsp;</p><p>Ingat bahwa penyelesaian persamaan "sin x = sin a" terdapat 2 penyelesaian, yaitu:</p><p>1. x = a + k.2π</p><p>2. x = (π-a) + k.2π</p><p>&nbsp;</p><p>sin 2x- ½√3=0</p><p>sin 2x = ½√3</p><p>sin 2x = sin (π/3)</p><p><strong>1. &nbsp;x = a + k.2π</strong></p><p>2x = (π/3) + k.2π &nbsp; &nbsp;(dibagi 2)</p><p>&nbsp; &nbsp;x = (π/6) + k.π</p><p>*k = 0 &nbsp;==&gt; x = π/6 &nbsp; &nbsp; (M)</p><p>*k= 1 &nbsp; ==&gt; x = 7π/6 &nbsp; (M)</p><p>*k= 2 &nbsp; ==&gt; x = 13π/6 (TM)</p><p><strong>2. x = (π-a) + k.2π</strong></p><p>2x = (π -π/3) + k.2π &nbsp; &nbsp;</p><p>2x = (2π /3) + k.2π &nbsp; &nbsp;(dibagi 2)</p><p>&nbsp; &nbsp;x = (π/3) + k.π</p><p>*k = 0 &nbsp;==&gt; x = π/3 &nbsp; &nbsp; (M)</p><p>*k= 1 &nbsp; ==&gt; x = 4π/3 &nbsp; (M)</p><p>*k= 2 &nbsp; ==&gt; x = 7π/3 &nbsp;(TM)</p><p>HP = {π/6, &nbsp;π/3, 7π/6, 4π/3}</p><p>&nbsp;</p><p>Jadi, himpunan penyelesaian persamaan trigonometri tersebut adalah &nbsp;{π/6, &nbsp;π/3, 7π/6, 4π/3}</p>