TRiGoNoMeTRi

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tan (2x + ¹/₃π) = ¹/₃√3

tan (2x + ¹/₃π) = tan ¹/₃π

       2x + ¹/₃π = ¹/₃π

                 2x = 0

x = α + k . π → rumus

2x = 0π + k . π

 x = 1/2 kπ

k = 0 → x = 0π

k = 1  → x = 1/2 π

k = 2 → x = π

k = 3 → x = 3/2π

k = 4 → x = 2π

HP = {0π , 1/2π , π , 3/2 π , 2π}

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2 cos² 3x - cos 3x - 1 = 0

misal p = cos 3x

2p² - p - 1 = 0

(2p + 1)(p - 1) = 0

maka p = -1/2 ∨ p = 1

jika p = -1/2

cos 3x = cos 2/3 π

      3x = 2/3 π

x = α + k . 2π → rumus

3x = 2/3 π + k .  2π

  x = 2/9 π + 2/3 kπ

k = 0 → x = 2/9 π

k = 1  → x = 8/9 π

k = 2 → x = 14/9 π

x = -α + k . 2π → rumus

3x = -2/3 π + k .  2π

  x = -2/9 π + 2/3 kπ

k = 1 → x = 4/9 π

k = 2 → x = 10/9 π

k = 3 → x = 16/9 π

jika p = 1 , maka :

cos 3x = 1

cos 3x = cos 0

      3x = 0

x = α + k . 2π → rumus

3x = 0π + k .  2π

 x = 2/3 kπ

k = 0 → x = 0π

k = 1  → x = 2/3 π

k = 2 → x = 4/3 π

k = 3 → x = 2π

maka,

HP = {0π , 2/9 π , 4/9 π , 6/9 π , 8/9 π , 10/9 π, 12/9 π , 14/9 π, 16/9 π, 2π}

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