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TRIGONOMETRI SUDUT RANGKAPI. RUMUS SUDUT RANGKAP DAN SUDUT PERSETENGAHAN

1. RUMUS SUDUT RANGKAP.(1) sin 2A = 2 sin A cos A(2) cos 2A = cos2A – sin2A

= 1 – 2 sin2A = 2 cos2A – 1

(3) tan 2A = A

A2tan1

tan2

(4) sin 3A = 3 sin A – 4 sin3A(5) cos 3A = 4 cos3A – 3 cos A

(6) tan 3A = A

AA2

3

tan31

tantan3

2. RUMUS SUDUT PERSETENGAHAN.

(1) sin 2

1A =

2

cos1 A

(2) cos2

cos1

2

1 AA

(3) tanA

AA

cos1

cos1

2

1

= A

A

cos1

sin

A

A

sin

cos1

1. a) sin 2 α = 2

2 tan

1 tan

b) cos 2 α =

2

2

1 tan

1 tan

2.

2 0

2 0

1 tan (45 )sin 2

1 tan (45 )

3. Jika cos α = 1/3 maka cos 2 α =…

4. . Jika sin α = 2/5 maka cos 2 α =…..5. Jika sin α = 3/5 maka sin 2 α = …..6. Jika α = 1/3 maka

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tan 2 α = ….7. Jika tan α = 1/7 berapakah nilai dari sin 2α dan cos 2α.8. Jika cos α = 4/5 makatan (1/2) α = …..9. Jika cos 2 α = 0.96 maka tan α =…..

10. sin 2

1 cos 2

= tan α

11.

sin 2

1 cos2

= cot α

12. 1 cos

sin

= tan

(1/2)α

13. 1 cos

sin

= cot (1/2)

α14. 2 cosec 2 α = sec α cosec α15. tan α + cot α = 2 cosec 2 α16. cos4 α – sin4 α = cos 2 α17. cot α – tan α = 2 cot 2 α

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18. cot 2 α =

2cot 1

2cot

19. cot tan

cot tan

= cos 2 α

20.

21 cot

2cot

= cosec 2

α

21.

2

2

cot 1

cot 1

= sec 2 α

22. 1 sec

sec

=

2 cos2 (1/2) α

23. sec 1

sec

=

2 sin2 (1/2) α

24.

2

2

2 sec

sec

=

cos 2 α

25.

2

2

cos 2

cos

ec

ec

= cos 2 α

26. ( sin (1/2) α + cos (1/2) α )2 = 1 + sin α27. ( sin (1/2) α - cos (1/2) α )2 = 1 – sin α

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28. cos 2

1 sin 2

=

tan (450 – α)

29. cos 2

1 sin 2

=

cot (450 – α)30. sin 8 α = 8 sin α cos α cos 2 α cos 4 α31. cos 4 α = 8 cos4 α – 8 cos2 α + 132. sin α = 1 – 2 sin2 (450

– ½ α)33. cos2 (

4

– α ) – sin2 (

4

– α ) = sin 2 α

34. tan ( 450 + α ) - tan ( 450 - α ) = 2 tan 2 α 35. tan ( 450 + α ) + tan ( 450 - α ) = 2 sec 2 α