Question

Tolong dibantu...pake caranya...makasih sebelumnya...

Answer 1

Nomor 1.
Gunakan sifat operasi sudut.

a.)
sin(π/2 + a)
= sin π/2 . cos a + cos π/2 . sin a
= 1 . cos a + 0 . sin a
= cos a

b.)
cos(π + a)
= cos π . cos a - sin π . sin a
= (-1) . cos a - 0 . sin a
= -cos a

c.)
tan(2π - a)
= [tan 2π - tan a] / [1 + tan 2π . tan a]
= [0 - tan a] / [1 + 0 . tan a]
= -tan a / 1
= -tan a

d.)
cos (-15)
= cos (30 - 45)
= cos 30 . cos 45 + sin 30 . sin 45
= 1/2 √3 . 1/2 √2 + 1/2 . 1/2 √2
= 1/4 √6 + 1/4 √2
= 1/4 √2 (√3 + 1)

e.)
sin 195
= sin(150 + 45)
= sin 150 . cos 45 + cos 150 . sin 45
= 1/2 . 1/2 √2 + (-1/2 √3) . 1/2 √2
= 1/4 √2 - 1/4 √6
= -1/4 √2 (√3 - 1)

f.)
tan 255
= tan (225 + 30)
= [tan 225 + tan 30] / [1 - tan 225 . tan 30]
= [1 + 1/3 √3] / [1 - 1. 1/3 √3]
= [1 + 1/3 √3] / [1 - 1/3 √3]
Kalikan dengan 3 ada pembilang dan penyebut:
= [3 + √3] / [3 - √3]
Rasionalkan:
= [3 + √3] / [3 - √3] x [3 + √3] / [3 + √3]
= (3 + √3)² / (9-3)
= (9 + 6√3 + 3) / 6
= (12 + 6√3) / 6
= 2 + √3