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RIANI WIDIASTUTI , S.Pd KELAS X TRIGONOMETRI

RIANI WIDIASTUTI , S.Pd KELAS X TRIGONOMETRI. RIANI WIDIASTUTI , S.Pd KELAS X TRIGONOMETRI. NEXT. MENU :. PERBANDINGAN TRIGONOMETRI SUDUT – SUDUT PADA SEMUA KUADRAN. R UMUS PERBANDINGAN TRIGONOMETRI UNTUK SUDUT – SUDUT BERELASI.

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RIANI WIDIASTUTI , S.Pd KELAS X TRIGONOMETRI

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  1. RIANI WIDIASTUTI , S.Pd KELAS X TRIGONOMETRI RIANI WIDIASTUTI , S.Pd KELAS X TRIGONOMETRI NEXT

  2. MENU : PERBANDINGAN TRIGONOMETRI SUDUT – SUDUT PADA SEMUA KUADRAN RUMUS PERBANDINGAN TRIGONOMETRI UNTUK SUDUT – SUDUT BERELASI RUMUS PERBANDINGAN TRIGONOMETRI UNTUK SUDUT – SUDUT LAINNYA MERUBAH KEDUDUKAN TITIK DARI KOORDINAT KUTUB DALAM KOORDINAT KARTESIUS MERUBAH KEDUDUKAN TITIK DARI KOORDINAT KARTESIUS DALAM KOORDINAT KUTUB Identitastrigonometri

  3. PERBANDINGAN TRIGONOMETRI SUDUT – SUDUT PADA SEMUA KUADRAN αberadapadakuadran 1 ( o °< α < 90°) maka : Sin α = cosec α = cosα = sec α = tan α = cot α = r y α x Contohsoal : Diketahui sin α = 4/5 padakuadran I tentukannilai cot αdancosα Jawab : Cos α = 3/5 cot α = 3/4 5 4 3

  4. αberadapadakuadran II ( 90 °< α < 180°) maka : Sin α = cosec α = cosα = sec α = tan α = cot α = r y α - x Contohsoal : Diketahuicosα = - 3/5 padakuadran II tentukannilai cot αdan cosec α Jawab : Cot α = - 3/4 cosec α = 5/4 5 4 - 3

  5. - x αberadapadakuadran III ( 180 °< α < 270°) maka : Sin α = cosec α = cosα = sec α = tan α = cot α = α - y r Contohsoal : Diketahuicosα = - 2/3 padakuadran III tentukannilai sin αdan tan α - 2 Jawab : Sin α = - /3 tan α = / 2 3

  6. x αberadapadakuadran IV ( 270°< α < 360°) maka : Sin α = cosec α = cosα = sec α = tan α = cot α = α - y r Contohsoal : Diketahuicosα = t padakuadran IV tentukannilai sin αdan sec α t 1 Jawab : Sin α = sec α = 1/t

  7. TIME OUTSENAM HOME

  8. RUMUS PERBANDINGAN TRIGONOMETRI UNTUK SUDUT – SUDUT BERELASI Sin ( 90 - α ) = = cosα cot ( 90 - α ) = = tan α cos ( 90 - α ) = = sin α cosec ( 90 - α ) = = sec α Tan ( 90 - α ) = = cot α sec ( 90 - α ) = = cosec α r y α x Sin ( 90 + α ) = = cosα cot ( 90 + α ) = - = - tan α cos ( 90 + α ) = - = - sin α cosec ( 90 + α ) = = sec α Tan ( 90 + α ) =- = - cot α sec ( 90 + α ) = - = - cosec α r y α x

  9. r y y - x α x Sin ( 180 - α ) = = sin α cot ( 180 - α ) = - = - cot α cos ( 180 - α ) = - = - cosα cosec ( 180 - α ) = = cosec α Tan ( 180 - α ) = - = - tanα sec ( 180 - α ) = - = - sec α r y - x α x - y Sin ( 180 + α ) = - = - sin α cot ( 180 + α ) = = cotanα cos ( 180 + α ) = - = - cosα cosec ( 180 + α ) = - = - cosec α Tan ( 180 + α ) = = tan α sec ( 180 + α ) = - = - sec α

  10. TIME OUTBERNYANYI HOME

  11. r y - x α x - y Sin ( 270 - α ) = - = - cosα cot ( 270 - α ) = = tan α cos ( 270 - α ) = - = - sin α cosec ( 270 - α ) = = - sec α Tan ( 270 - α ) = = cotα sec ( 270 - α ) = - = - cosec α

  12. Sin ( 270 + α ) = - cosα cot ( 270 + α ) = - tan α cos ( 270 + α ) = sin α cosec ( 270 + α ) = - sec α Tan ( 270 + α ) = - cotanα sec ( 270 + α ) = cosec α Sin ( 360 - α ) = - sin α cot ( 360 - α ) = - cot α cos ( 360 - α ) = cosα cosec ( 360 - α ) = - cosec α Tan ( 360 - α ) = - tan α sec ( 360 - α ) = sec α

  13. LATIHAN : Hitunglahnilaidari : a. Sin 315° b. Cos 210° c. Tan 240° 2. Sederhanakanbentukberikut : a. b. 3. Diketahui sin 40°= n . Tentukannilaidari tan 230° dan cot 320° BACK

  14. Rumus – rumusperbandingantrigonometriuntuksudut ( - α ) Sin ( - α ) = - sin α cot ( - α ) = - cot α cos ( - α ) = cosα cosec ( - α ) = - cosec α Tan ( - α ) = - tan α sec ( - α ) = sec α Rumus – rumusperbandingantrigonometriuntuksudut ( n. 360° - α ) Sin ( n. 360° - α ) = - sin α cot ( n. 360° - α ) = - cot α cos ( n. 360° - α ) = cosα cosec (n. 360° - α ) = - cosec α Tan ( n. 360° - α ) = - tan α sec ( n. 360° - α ) = sec α

  15. Rumus – rumusperbandingantrigonometriuntuksudut ( n. 360° + α ) Sin ( n. 360° + α ) = sin α cot ( n. 360° + α ) = cot α coos ( n. 360°+α ) = cosα cosec (n. 360° + α ) = cosec α Tan ( n. 360° + α ) = tan α sec ( n. 360° + α ) = sec α BACK

  16. MERUBAH KEDUDUKAN TITIK DARI KOORDINAT KUTUB DALAM KOORDINAT KARTESIUS Cos α = x/r x = r. Cos α Sin α = y/r y = r. sin α r y Jadi A ( r , α ° ) = A ( r. cosα° , r. sin α° ) α x Contoh : 1. A ( 10 , 60° ) x = r. Cos α° y = r . sin α°jadi A ( 5, 5 ) = 10 . Cos 60° = 10 . Sin 60° = 10. ½ = 10 . ½ = 5 = 5 Contoh : 2. B ( 20 , 120° ) x = r. Cos α° y = r . sin α°jadi B ( - 10 , 10 ) = 20 . Cos 120° = 20 . Sin 120° = 20 . ( - ½ ) = 20 . ½ = - 10 = 10 BACK

  17. MERUBAH KEDUDUKAN TITIK DARI KOORDINAT KARTESIUS DALAM KOORDINAT KUTUB x² + y² = r² r = Tan α = y/x αdapatditentukan r y Jadi A ( x , y ) = A ( , arc tan y/x ) α x Contoh : 1. A ( 5 , 5 ) Dikuadran 1 x² + y² = r² ( 5 )² + 5² = r² 75 + 25 = r² = r² r = 10 jadi A ( 10 , 30º ) dikuadran I Contoh : 2. A ( 5 , - 5 ) Dikuadran 1V x² + y² = r² ( 5 )² + ( - 5) ² = r² 75 + 25 = r² = r² r = 10 jadi A ( 10 , 330º ) dikuadran IV

  18. LATIHAN SOAL : Nyatakandalamkoordinatkartesius a. A ( 10 , 315° ) b. B ( 5 , 225° ) 2. Nyatakandalamkoordinatkutub a. A ( - 1 , -1 ) b. B ( - 8 , 8 ) BACK

  19. IDENTITAS TRIGONOMETRI Tan A = 5. cos²A + sin²A = 1 2. Cot A = 6. 1 + tan²A = sec²A Sin A = 7. 1 + cot²A = cosec²A 4. cos A = 8. Tan² A = Contoh : Buktikan Cos²A – sin²A = 2 cos²A- 1 5. Jika p – q = cos A = sin A maka p² + q² = 1 2. Cos²A – sin²A = 1 – 2sin²A 3. Sin A . Cot A = cos A 4. = cosec A + cot A BACK

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