BAB TRIGONOMETRI kelas 11
Jawab:
trigonometri
rumus jumlah dan perkalian
cos (A + B) = cos A cos B – sin A sin B
Penjelasan dengan langkah-langkah:
i) cos (22,5 -a ) cos (22,5 + a) - sin (22,5 -a )(sin 22,5 + a) =
A= 22,5 + a dan B = 22,5 – a
cos B cosA - sin B sin A = cos (A + B)
= cos (22,5 -a + 22,5 + a)
= cos 45
= 1/2 √2
2) cos (π/2 +a) cos (π/6 +a) – sin (π/2 +a) sin (π/6 +a) =
= – sin a cos (π/6 +a) – cos a sin (π/6 +a)
= – (sin a cos (π/6 +a) + cos a sin (π/6 +a))
= – sin (a + π/6 +a)
= – sin (2a+ π/6)
= – { sin 2a cos π/6+ cos 2a sin π/6)
= – { sin2a (1/2√3 ) + cos 2a ( 1/2)}
= – 1/2 (√3 sin 2a + cos 2a)
a]
cos (x + y) = cos x cos y – sin x sin y
soal tulis kembali
= cos (22,5 – a + 22,5 + a)°
= cos 45°
= 1/2 √2
b]
soal
= cos (π/2 + a + π/6 + a)
= cos (2a + 90° + 30°)
= cos (2a + 120°)
= cos 2a cos 120° – sin 2a sin 120°
= cos 2a . (-1/2) – sin 2a . (1/2 √3)
= -1/2 (cos 2a + √3 sin 2a)