Jika cos 150° = p, maka nilai dari sin 75° =… (+caranya)

TRIGONOMETRI
– sudut rangkap

cos 150° = p
sin 75° = __ ?

cos 2x = 1 – 2 sin² x
2 sin² x = 1 – cos 2x
sin² x = (1 – cos 2x) /2
sin x = √[(1 – cos 2x) /2]

untuk x = 75°, 2x = 150°
sin x = √[(1 – cos 2x) /2]
sin 75° = √[(1 – cos 150°) /2]
sin 75° = √[(1 – p) /2]  ← jwb

Cos 150 = p
– cos (180-30) = p
– cos 30 = p
– 1/2√3 = p

sin 75 = 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√2 (√3 + 1)
= -p/2 √2 (√3+1) jika dinyatakan dlam p