Jawab:
[1.]  Hp = {45°, 135°, 225°, 315°}
[2.] Hp = {30°, 150°}
[3.] Hp = {95°, 275°}
[4.] Hp = {45°, 105°}

Penjelasan dengan langkah²:
[1.]  6 sin² x = 3  {0° ≤ x ≤ 360°}
sin² x = ³/₆       sin² x = ½
|sin x| = √(½)   |sin x| = ½√2
sin x = ±½√2
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Nilai sin⁻¹ positif dan negatif
Hp ada di semua 4 kuadran.
x = {sin⁻¹ (sin x), 180°-sin⁻¹ (sin x),
180°+sin⁻¹ (sin x), 360°-sin⁻¹ (sin x)}
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Periodisitas sin x = 360°, maka
ada 4 penyelesaian.
sin x = ±½√2
sin⁻¹ ½√2 = 45°, maka
x = {sin⁻¹ ½√2, 180°-sin⁻¹ ½√2,
180°+sin⁻¹ ½√2, 360°-sin⁻¹ ½√2}
x = {45°, 180°-45°, 180°+45°, 360°-45°}
x = {45°, 135°, 225°, 315°}
Hp = {45°, 135°, 225°, 315°}

[2.]  4 sin x = 2  {0° ≤ x ≤ 360°}
sin x = ²/₄   sin x = ½
Nilai sin⁻¹ positif, di kuad i dan ii
x = {sin⁻¹ (sin x), 180° - sin⁻¹ (sin x)}
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Periodisitas sin x = 360°, maka
ada 2 penyelesaian.
sin⁻¹ ½ = 30°, maka
x = {sin⁻¹ ½, 180° - sin⁻¹ ½}
x = {30°, 180° - 30°}
x = {30°, 150°}
Hp = {30°, 150°}

[3.]  sin(40°+x) + cos(40°+x) = 0
{0° ≤ x ≤ 360°}

tan(40°+x) + 1 = 0
tan(40°+x) = -1
40°+x = tan⁻¹(-1)
Nilai tan⁻¹ negatif di kuad ii dan iv
40°+x = 180° - tan⁻¹(1) = 360° - tan⁻¹(1)
tan⁻¹(1) = 45°, maka
40°+x = 180° - 45° = 360° - 45°
40°+x = 135° = 315°
x = {135° - 40°, 315° - 40°}
x = {95°, 275°}
Hp = {95°, 275°}

[4.]  cos(x-75°) = ½√3  {0° ≤ x ≤ 360°}
x-75° = cos⁻¹(½√3)
nilai cos⁻¹ positif di kuad i dan iv
cos⁻¹(½√3) = 30°, maka
x-75° = cos⁻¹(½√3) = 0° - cos⁻¹(½√3)
x-75° = 30° = 0° - 30°
x-75° = 30° = -30°
x = {30°+75°,  -30°+75}
x = {105°, 45°}
Hp = {45°, 105°}

(xcvi)