Nilai x yang memenuhi persamaan sin (2x - 30⁰) = cos(x + 60⁰) pada interval 0⁰≤x≤ 360⁰ adalah... a. 20⁰, 140⁰, 180⁰, 260⁰ b. 20⁰, 160⁰, 180⁰, 240⁰ C. 40°, 140°, 220°, 320° d. 40⁰, 160⁰, 200⁰, 260⁰ e. 20⁰, 160⁰, 180⁰, 300⁰

<p>Jawabannya adalah a. 20⁰, 140⁰, 180⁰, 260⁰</p><p>&nbsp;</p><p>Ingat!</p><p>sin x = sin A</p><p>x = A + k.360°</p><p>atau</p><p>x = (180 - A) + k.360°</p><p>cos 𝞪 = sin (90° - 𝞪)</p><p>&nbsp;</p><p>Jawab:</p><p>sin (2x - 30°) = cos (x + 60°)</p><p>sin (2x - 30°) = cos (90° - (30° - x))</p><p>sin (2x - 30°) = sin (30° - x)</p><p>&nbsp;</p><p><strong>sin x = sin A</strong></p><ol><li><strong>x = A + k.360°</strong><br>(2x - 30°) = (30° - x) + k.360°<br>2x + x = 30° + 30° + k.360°<br>3x = 60° + k.360... (i)<br>x = 20° + k.120°</li><li><strong>x = (180 - A) + k.360°</strong><br>&nbsp;(2x - 30°) = (180 - (30° - x)) + k.360°<br>(2x - 30°) = (150 + x) + k.360°<br>2x - x = 150° + 30° + k.360°<br>x = 180° + k.360°...(ii)</li></ol><p>&nbsp;</p><ul><li>Menentukan nilai x<br>a. k = 0<br>i) x = 20° + k.120°<br>x = 20° + 0 . 120°<br><strong>x = 20°</strong><br>ii) x = 180° + k.360°<br>x = 180° + 0 .360°<br><strong>x = 180°</strong><br><br>b. k =1<br>i) x = 20° + k.120°<br>x = 20° + 1 . 120°<br><strong>x = 140°</strong><br>ii) x = 180° + k.360°<br>x = 180° + 1 . 360°<br>x = 540° ... Tidak memenuhi<br><br>c. k = 2<br>i) x = 20° + k.120°<br>x = 20° + 2 . 120°<br><strong>x = 260°</strong><br><br>d. k = 3<br>i) x = 20° + k.120°<br>x = 20° + 3 . 120°<br>x = 380°... Tidak memenuhi</li></ul><p>&nbsp;</p><p>Jadi, nilai x yang memenuhi persamaan sin (2x - 30⁰) = cos(x + 60⁰) pada interval 0⁰≤x≤ 360⁰ adalah a. 20⁰, 140⁰, 180⁰, 260⁰</p>