trigonometri

RUMUS TRIGONOMETRI

OLEH

IBNU NUGROHO

085 742 151 433

 

Cosec= Sec     = Cot     =

Sin x              =  

      DE           Cos x               =

Tang x           =

MI

                                    SA

                                   

                           

                            II                 I

                            + sin          + all

                            + tang       + cos

                            III               IV

Sudut Istimewa

a	0o	30o	45o	60o	90o
sin a	0				1
cos a	1				0
tan a	0		1		-

Identitas

1. sin² x + cos2 x = 1

2. sin2 x = 1  cos2 x

3. cos² x = 1  sin2 x

4.

5. sec2 x = tan2 x + 1

6. csc2 x = cot2 x + 1

Luas segi tiga s = ½ (a + b + c)

1.        Persamaan trigonometri: Persamaan dasar sinus: sin x = sin α x = α + k . 360 x = 180 – α + k . 360 Persamaan dasar cosinus: cos x = cos α x = α + k . 360 x = – α + k . 360 Persaman dasar tangen: tan x =  tan α x = α + k . 180

Aturan sinus

Aturan cosines

Rumus Trigonometri

	Bentuk a cos x + b sin x 1. a cos x + b sin x = k cos (x- α)             K= 2. y = a cos x + b sin x + c ymax = k + c dan ymin =  k + c 3. Agar acos x + bsin x = c bisa diselesaikan maka + ≥

 

1. sin (α + ß) = sin α cos ß + cos α sin ß

2. sin (α -ß) = sin α cos ß -cos α sin ß

3. cos (α + ß) = cos α cos ß -sin α sin ß

4. cos (α -ß) = cos α cos ß + sin α sin ß

5.

7. sin 2 α = 2 sin α cos α

8. cos 2 α = cos2 α -sin2 α

cos 2 α = 2cos2 α -1

cos 2 α = 1- 2sin2 α

9. sin 3 α = 3sin α- 4sin3 α

10. cos 3 α = 4cos3 α- 3cos α

11. 2sin α cos α = sin (α + α) + sin (α - α)

12. 2cos α sin α = sin (α + α)- sin (α- α)

13. 2 cos α cos α = cos (α + α) + cos (α- α)

14. –2sin α cos α = cos (α + α)- cos (α- α)

15. sin α + sin α = 2 sin (α + α) cos (α- α)

16. sin α  sin α = 2 cos  (α + α) sin (α- α)

18. cos α + cos α = 2cos (α + α) cos (α- α

19. cos α  cos α = 2 sin  (α + α) sin (α- α

RUMUS TRIGONOMETRI

OLEH

IBNU NUGROHO

085 742 151 433

 

Cosec= Sec     = Cot     =

Sin x              =  

      DE           Cos x               =

Tang x           =

MI

                                    SA

                                   

                           

                            II                 I

                            + sin          + all

                            + tang       + cos

                            III               IV

Sudut Istimewa

a	0o	30o	45o	60o	90o
sin a	0				1
cos a	1				0
tan a	0		1		-

Identitas

1. sin² x + cos2 x = 1

2. sin2 x = 1  cos2 x

3. cos² x = 1  sin2 x

4.

5. sec2 x = tan2 x + 1

6. csc2 x = cot2 x + 1

Luas segi tiga s = ½ (a + b + c)

1.        Persamaan trigonometri: Persamaan dasar sinus: sin x = sin α x = α + k . 360 x = 180 – α + k . 360 Persamaan dasar cosinus: cos x = cos α x = α + k . 360 x = – α + k . 360 Persaman dasar tangen: tan x =  tan α x = α + k . 180

Aturan sinus

Aturan cosines

Rumus Trigonometri

	Bentuk a cos x + b sin x 1. a cos x + b sin x = k cos (x- α)             K= 2. y = a cos x + b sin x + c ymax = k + c dan ymin =  k + c 3. Agar acos x + bsin x = c bisa diselesaikan maka + ≥

 

1. sin (α + ß) = sin α cos ß + cos α sin ß

2. sin (α -ß) = sin α cos ß -cos α sin ß

3. cos (α + ß) = cos α cos ß -sin α sin ß

4. cos (α -ß) = cos α cos ß + sin α sin ß

5.

7. sin 2 α = 2 sin α cos α

8. cos 2 α = cos2 α -sin2 α

cos 2 α = 2cos2 α -1

cos 2 α = 1- 2sin2 α

9. sin 3 α = 3sin α- 4sin3 α

10. cos 3 α = 4cos3 α- 3cos α

11. 2sin α cos α = sin (α + α) + sin (α - α)

12. 2cos α sin α = sin (α + α)- sin (α- α)

13. 2 cos α cos α = cos (α + α) + cos (α- α)

14. –2sin α cos α = cos (α + α)- cos (α- α)

15. sin α + sin α = 2 sin (α + α) cos (α- α)

16. sin α  sin α = 2 cos  (α + α) sin (α- α)

18. cos α + cos α = 2cos (α + α) cos (α- α

19. cos α  cos α = 2 sin  (α + α) sin (α- α