Nama : Ulfa Mustofa Nurfadilasari

Kelas : XI IPA 5

Rumus Trigonometri Perkalian Sinus dan Kosinus

(i) 2sin α cos β = sin (α+ β) + sin ( α- β )

(ii) 2 cos α sin β = sin (α+ β) – sin (α - β)

(iii) 2 cos α cos β = cos (α+β) + cos(α+ β)

(iv) -2 sin α sinβ = cos (α +β ) – cos (α- β)

2sin α cos β = sin (α+ β) + sin ( α- β )

1. Nilai dari sin 75⁰ cos 15⁰= . . .

Jawab :

sin 75⁰cos 15⁰ =½ sin (75⁰+ 15⁰ ) +sin (75⁰-15⁰)

= ½ sin (90⁰+ 60⁰)

= (

=

=

2. Nilai dari sin 7 ½ ⁰ cos 37 ½ ⁰ = …

Jawab:

Sin 7½ ⁰ cos 37 ½ ⁰ = ½ (sin (7 ½ ⁰ + 37 ½ ⁰) - sin (7 ½ ⁰ - 37 ½ ⁰) )

= ½ sin (45⁰- (-30⁰)

=

=

=

3. Nilai dari sin 120⁰ cos 60⁰ = …

Jawab:

Sin 120 ⁰ cos 60⁰ = ½ (sin (120⁰ + 60⁰) + sin (120⁰- 60⁰)

= ½ sin 180⁰ + 60⁰

=

=

2 cos α sin β = sin (α+ β) – sin (α - β)

4. Nilai dari cos 82 ½ ⁰ sin 37 ½ ⁰ = …

Jawab:

cos 82 ½ ⁰ sin 37 ½ ⁰ = ½ (2 cos 82 ½ ⁰ sin 37 ½ ⁰)

= ½ {sin ( 82 ½ ⁰ + 37 ½ ⁰) – sin (82 ½ ⁰ - 37 ½ ⁰)}

= ½ (sin 120⁰ - 45⁰)

=

=

=

5. Nilai 2 cos 75⁰ sin 5⁰= . . .

Jawab:

2cos 75⁰ sin 5⁰= sin (75⁰ + 5⁰) –sin (75⁰-5⁰)

= sin 80⁰ - sin 70⁰

2 cos α cos β = cos (α+β) + cos(α+ β)

6. Hitunglah cos 75⁰ cos 15⁰= …

Jawab:

cos 75⁰ cos 15⁰= ½ (cos (75⁰+15⁰) + cos (75⁰- 15⁰)

= ½ (cos 90⁰ + 60⁰)

= ½ (0 + ½ )

= ¼

7. Hitunglah cos 105⁰ cos 15⁰= . . .

Jawab:

Cos 105⁰ cos 15⁰ = ½ (cos (105⁰+15⁰) + cos (105⁰-15⁰)

= ½ cos (120⁰ + 90⁰)

= ½ ( ½ . 0)

= - 1/4

-2 sin α sinβ = cos (α +β ) – cos (α- β)

8. Nilai -2 sin 15⁰ sin 75⁰ = . . .

Jawab:

-2 sin 15⁰ sin 75⁰= cos (15⁰+75⁰) –cos (15⁰-75⁰)

= cos 90

=0 – ½

= ½

9. Nilai dari -2 sin 50⁰sin 40⁰= . . .

Jawab:

-2 sin 50

= cos 90

= 0

= cos 10

10. Nilai -2 sin 97,5⁰ sin 127,5⁰ = . . .

Jawab:

-2 sin 97,5⁰sin 127,5⁰= cos (97,5⁰+ 127,5⁰) –cos (97,5⁰-127,5⁰)

= cos 225

=

=

= 0 (

=

11. Nilai

Jawab:

-2 sin 120

= cos 210

= (

=

` =