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Matematika


1. Menentukan Himpunan Penyelesaian {HP}

• Sin X⁰ = 1/2 V3 , 0 < X < 300
  penyelesaian : Sin X⁰= Sin 1/2V3
  sin x = sin 60
  sin x = 60+k.360
  k --> 0 = 60+ (0)360 = 60
  k--> -1 = 60+(-1)360 = -300
  HP = {60;300}
• Cos X⁰= 4/5 , 0 < X < 300
  Cos x = Cos 0,8
  Cos x = Cos 36⁰,52'
  Cos x = 36,09⁰
  Cos x = 36,09 + k.360
  k ----> 0 = 36,09 + (0) 360= 36,09
  k-----> -1 = 36,09 + (-1)360 = -323,91
  HP = {36,09 ; -323,91}
• Sin X⁰ = -1/2 , 0< X < 2π
  Sin x = - Sin 30
  Sin x = Sin (180+30)
  Sin x = sin 210
  Sin x = 210+k.360
  k --> 0 = 210
  k --> -1 = 210 + (-1)360 = -150
  HP = { 210 ; -150}
• Cos X⁰=  -1/2 V2 , 0< X  < 2π
  2π = 2x180 = 360Cos x = Cos -1/2
  Cos x = -Cos 60
  Cos x = Cos (180-60)
  Cos x = Cos 120Cos x = 120 + k.360
  k --> 0 = 120
  k --> -1 = 120+ (-1) 360= -240
  HP = {120 ; -240 }
•  Tan X⁰= 1/V3  , 0 < X < ππ = 180
  Tan x = Tan 1/3 V3
  Tan x = Tan 30
  Tan x = 30 + k.360
  k --> 0 = 30
  k --> -1 = 30 + (-1) 360 = -330
  HP = { 30 ; -330 }
• Tan X⁰= -V3 , 0 < X < 300
  Tan x = - Tan 60
  Tan x = Tan (180-60)
  Tan x = Tan 120
  Tan x = 120 + k.360
  k --> 0 = 120
  k --> -1 = 120 + (-1)360= - 240
  HP = { 120 ; -240 }

2. Tentukan ( X = ) 0 < X < 360 {tugas}

• Sin X⁰ = -3/5
• Sin X⁰ = 0, 3616
• Cos X⁰ + 1 = 0
• Cos X⁰ = 2/3
• Tan X⁰ + 1/V3 = 0
• Tan X⁰ = 1,5204

Notes :
π = 180