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TRIGONOMETRI

TRIGONOMETRI. IDIKATOR: MEMBUKTIKAN KESAMAAN TRIGONOMETRI MENYEDERHANAKAN PERSAMAAN TRIGONOMETRI SERTA MENCARI PENYELESAIAN PERSAMAAN DAN PERTIDAKSAMAAN. BY : ULIYA FATIMAH (09320008). TRIGONOMETRI. MATERI: Perbandingan Trigonometri dan Teorema Pythagoras

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TRIGONOMETRI

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  1. TRIGONOMETRI IDIKATOR: MEMBUKTIKAN KESAMAAN TRIGONOMETRI MENYEDERHANAKAN PERSAMAAN TRIGONOMETRI SERTA MENCARI PENYELESAIAN PERSAMAAN DAN PERTIDAKSAMAAN BY : ULIYA FATIMAH (09320008)

  2. TRIGONOMETRI MATERI: Perbandingan TrigonometridanTeorema Pythagoras Nilai Perbandingan Trigonometri untuk Sudut Istimewa Perbandingan Trigonometri dalam Kuadran Identitastrigonometri

  3. TRIGONOMETRI Perbandingan Trigonometri& Teorema Pythagoras Ketahuilah , pada Pythagoras hanya berlaku pada segi tiga siku-siku dan sisimiring atau disebut dengan hipotenusa sama dengan jumlah padakeduasisisiku-sikusegitiga.

  4. TRIGONOMETRI AC2 = AB2+ BC2 C Contoh: Hitunglah panjang sisi x yang belum diketahui, pada segitiga siku-siku di samping ini (panjang segitiga dalam cm) HIPOTENUSA X B A jawab

  5. TRIGONOMETRI Jawab: C AC2 = AB2 + BC2 X2 = 122 + 52 = 144 + 25 = 169 X = 13 HIPOTENUSA X 15 B A 5

  6. TRIGONOMETRI C Sin α = Cos α = HIPOTENUSA Tan α = B A

  7. TRIGONOMETRI C cosec α = HIPOTENUSA Sec α = Cotan α = B A

  8. TRIGONOMETRI contoh: 1. Di titik R (8, 15) membentuksudut α, tentukan sec α ? Sec α = r2= x2 + y2 = 82 + 152 = 64 + 225 r y = 15 = α r = 17 x = 8 Sec α = 17 /8

  9. TRIGONOMETRI 2. Nilai Perbandingan Trigonometri untuk Sudut Istimewa

  10. TRIGONOMETRI Contoh: Buktikan sin245 + cos245 = 1 jawab: sin245 + cos245 = 1 (½ )2 + (½)2 = 1 ¼ 2 + ¼ 2 = 1 2/4 + 2/4 = 1 4/4=1 Terbukti, sin245 + cos245 = 1

  11. TRIGONOMETRI 3 PERBANDINGAN TRIGONOMETRI DALAM KUADRAN

  12. TRIGONOM ETRI

  13. TRIGONOMETRI sin α = = = = + Kuadran II Kuadran I r= + r= + y = + y = + x = + α α x = - y = - y = - r=+ r = + Kuadran IV Kuadran III

  14. TRIGONOM ETRI Contoh: • Cos α = -4/5 dan tan α positif, berapa nilai sin αsin .... sin α = = x = -4 α y2 = r2 - x2 y2 = 52 – (-4)2 y2 = 25 – 16 = y = -3 y = ? r = 5 Jadi, Sin α =

  15. TRIGONOM ETRI Contoh: • Cos α = -4/5 dan tan α positif, berapa nilai sin αsin .... sin α = = x = -4 y2 = r2 - x2 y2 = 52 – (-4)2 y2 = 25 – 16 = y = -3 α y = ? r = 5 Jadi, Sin α =

  16. TRIGONOMETRI 4 IDENTITAS TRIGONOMETRI

  17. TRIGONOMETRI Sin α = = cos α = = tan α = = cosec α = = Sec α = = cotann α = =

  18. TRIGONOM ETRI Hubungan antar pembanding a. Cosec α = b. Sec α = c. Cotan α =

  19. TRIGONOMETRI a. Cosec α = Cosec α = Cosec α = b. Sec α = Sec α = Sec α = c. Cotan α = Cotan α = Cotan α =

  20. TRIGONOMETRI 2. IdentitasdariHubunganTeorema Pythagoras (x2 + y2 = r2 ) a) x2 + y2 = r2(sama-sama dibagi r2) x2 / r2 + y2 / r2 = r2 / r2 x2 / r2 + y2 / r2 = 1 cos2 α + sin2 α = 1

  21. TRIGONOMETRI 2. IdentitasdariHubunganTeorema Pythagoras (x2 + y2 = r2 ) b) x2 + y2 = r2(sama-sama dibagi y2) x2 / y2 + y2 / y2 = y2 / y2 x2 / y2 + y2 / y2 = 1 cotan2α+1= cosec2 α

  22. TRIGONOMETRI Contoh 1 : jika 2 sin2 x + 3 cos x = 0 dan 0° < x < 180° maka nilaix adalah............. Jawab : 2 sin2 x + 3 cos x = 0 2(1- cos2 x) + 3 cos x = 0 2cos2 x - - 3 cos x - 2 = 0 (2 cos x + 1 ) ( cos x – 2 ) = 0 Cos x = - ½ cos x = 2 (tidak memenuhi)

  23. TRIGONOMETRI Contoh 2: Dari pertidaksamaan berikut sinx . sin2 x + cos2x < ½ berapakah nilai dari x Jawab: sinx . sin2 x + cos2x < ½ sin x .(sin2 x + cos2x) < ½ sin x . 1 < ½ sin x < ½ x< 30°

  24. TERIMAKASIH SEMOGA YANG KITA PELAJARI DAPAT BERMANFAAT AMIIIIIIN..

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