Persamaan Trigonometri

no. 1

tan 2x = tan 50°

2x = 50° + k.180°

x = 25° + k.90°

k bilangan bulat

k = 0 → x = 25°

k = 1 → x = 115°

dan seterusnya

Interval [0° , 360°]

HP = {25°, 115°, 205°, 295°}

no. 2

tan 4x = -√3

kuadran II

4x = 180° - 60° + k.180°

x = (120° + k.180°)/4

x = 30° + k.45°

k bilangan bulat

k = 0 → x = 30°

k = 1 → x = 30° + 45° = 75°

k = 2 → x = 30° + 90° = 120°

dan seterusnya

Interval [0° , 360°]

HP = {30°, 75°, 120°, 165°, 210°, 255°, 300°, 345°}

•

no. 3

π = 180°

tan (3x - 60°) = cot 2x

tan (3x - 60°) = tan (90° - 2x)

3x - 60° = 90° - 2x + k.180°

3x + 2x = 90° + 60° + k.180°

5x = 150° + k.180°

x = 30° + k.36°

x = π/6 + π/5 k

k bilangan bulat

k = 0 → x = π/6

k = 1 → x = 11π/30

dan seterusnya

Interval [0 , 2π]

HP = {π/6, 11π/30, 17π/30, 23π/30, 29π/30, 35π/30, 41π/30, 47π/30, 53π/30, 59π/30}