Jawab:

1×1=1

2×2=4

a cos x + b sin x = k cos (x - α)

k = √(a² + b²)

α = arc tan (b/a)

•

√3 cos x + sin x - √2 = 0

√3 cos x + sin x = √2

sin (+), cos (+) → kuadran I

k = √((√3)² + 1²) = 2

α = arc tan (1/√3) = 30°

√3 cos x + sin x = √2

2 cos (x - 30°) = √2

cos (x - 30°) = 1/2 √2

•

x - 30° = 45° + k.360°

x = 75° + k.360° ... (1)

•

x - 30° = -45° + k.360°

x = -15° + k.360° ... (2)

k bilangan bulat

k = 0 → x = -15° , x = 75°

k = 1 → x = 345° , x = 435°

dan seterusnya

interval 0° ≤ x ≤ 360°

HP = {75° , 345°}

soal (b)

sin 4x = cos x

sin 4x = sin (90° - x)

4x = 90° - x + k.360°

5x = 90° + k.360°

x = 18° + k.72° ... (1)

sin 4x = cos x

sin 4x = sin (90° + x)

4x = 90° + x + k.360°

3x = 90° + k.360°

x = 30° + k.120° ... (2)

k bilangan bulat

k = 0 → x = 18° , x = 30°

dan seterusnya

interval 0° ≤ x ≤ 360°

HP = {18° , 30° , 90° , 150° , 162° , 270° , 234° , 306°}

Penjelasan dengan langkah-langkah: