Jawaban:

[TRIGONOMETRI]

Penjelasan dengan langkah-langkah:

Sin (3x+2y) = 1/3

Cos (3x-4y) = 3/4

Nilai

Sin 6y = ....

Cos 9x

MISALKAN

(3x+2y) = α

(3x-4y) = β

6y = (3x+2y)-(3x-4y) = α-β

9x = 2(3x+2y)+(3x-4y)= 2α+β

Sin α = 1/3

Cos β = 3/4

Maka

Cos α = x/r = 2√2

3

Sin α = y/r = 1/3

x = √(r )²-(y)²

= √(3 )²-(1)²

= √(9 )-(1)

= √(8 )

= 2√(2)

Cos β = 3/4 = x/r

Sin β = y/r = √7 /4

y = √(r )²-(x)²

= √(4 )²-(3)²

= √(16 )-(9)

= √(7)

Sin 6y = α - β

Sin (α - β) = Sin α. Cos β - Cos α. Sin β

= (1/3. 3/4) - (2√2)/3.√7/4

= (3/12) - (2√14 )/12

= (3-2√14)/12

Cos 9x = 2α+β

Cos (2α+β) = Cos 2α Cos β - Sin 2α Sin β

=(Cos²α - Sin²α ). Cos β - (2 Sin α.Cosα).Sin β

= [2√2)² - (1/3)².3/4] - [2.1/3. 2√2 ).√7/4 ]

3 3

= (4.2) - (1/9) . 3/4 ] - ( 2/3 . 2√2 ).√7/4 )

9 3

= (8/9-1/9).3/4] - (4√2 ).√7/4]

9

= (7/9).3/4] - (4√14 )

36

= [21/36] - (4√14 )

36

= 21-4√14 )

36

Cos 2α = Cos²α - Sin²α

= 1 - 2 Sin²α

= 2 Cos²α-1

Sin 2α = 2 Sin α.Cosα

Maka:

Sin 6y = (3-2√14 )/12

Cos 9x = 21-4√14 )/36

(3-2√14 )/12

(21-4√14 )/36

(3-2√14 ) x 36

12. (21-4√14 )

3(3-2√14 )

(21-4√14 )

9-6√14 )

(21-4√14 )

⇒Opsi A.

Detail Jawaban:

Mapel : Matematika

Kelas : XI / 11 SMA

Materi : Trigonometri

Kode kategorisasi : -

Kata Kunci : Trigonometri