Question

Soalnya trigonometri.

1) Tunjukkan bahwa Sin 345 = 1/4√2 (1-√3)

2) Buktikan bahwa Sin (P+Q) + Sin (P+Q) = 2 Sin P Cos Q

TL Note: Sisanya lihat di gambar.

Answer 1

Verified answer

Jawab 2 soal saja
(1) sin 345 =  sin (360 - 15) = - sin 15
= - sin (45-30)
= - { sin 45  cos 30 - cos 45 sin 30}
= - ( 1/2 √2 . 1/2 √3  - 1/2 √2 . 1/2)
= - (1/4 √6 - 1/4 √2)
= -1/4 √6 + 1/4 √2
= 1/4 √ 2 ( - √3 +1)
= 1/4 √2 ( 1 - √3)

(2)  sin (P+Q) + sin (P -Q) =
= 2 sin 1/2 { P+Q+P-Q)  cos 1/2 (P+Q -P+Q)
= 2 sin 1/2 (2P)  cos 1/2 (2Q)
= 2 sin P cos Q