PEMBAHASAN

Trigonometri

tan (180° - α) = -2/√5

- tan α = - 2/√5

tan α = y/x = 2/√5

r = √(x² + y²) = √((√5)² + 2²) = 3

sin (180° - α) = sin α = y/r = 2/3

sin (270° - α) = - cos α = -x/r = -√5 /3

tan (360° - α) = - tan α = -2/√5

sin (-α) = - sin α

sin (2k + α) = sin α

sin (180° + α) = - sin a

sin (-960°)

= - sin (2×360° + 240°)

= - sin 240°

= - sim (180° + 60°)

= - (- sin 60°)

= sin 60°

= 1/2 √3

cosec (270° - α)

= 1/sin (270° - α)

= 1/(- cos α)

= 1/(-√5 /3)

= -3/√5

••

soal

= [2√3 (1/2 √3)² - 1/3 √3 (-2/√5)] / [1/4 √3 (2/3)² × (-3/√5)³]

= [2√3 × 3/4 + 2/15 √15] / [1/4 √3 × 4/9 × -27/(5√5)]

= [3/2 √3 + 2/15 √15] / [-2/25 √15]

pembilang dan penyebut dibagi dengan (√3)

= [3/2 + 1/15 √5] / [-2/25 √5]

pembilang dan penyebut kalikan dengan (150√5)

= - [225√5 + 50] / 60

= - [45√5 + 10]/12