Penjelasan dengan langkah-langkah:

TRIGONOMETRI

11. A

sin ß = ⅔

x = √(3²–2²)

x = √(9-4)

x = √5

cos ß = √5 ✔

3

12. A

sin 150° + sin 120°

cos 210° – cos 300°

= ½ + ½√3

–½√3 + ½

= ½(1 + √3)

½(1 – √3)

= (1 + √3)²

1² – (√3)²

= 1 + 3 + 2√3

1 – 3

= 2(2 + √3)

–2

= –(2 + √3)

= –2 – √3 ✔

13. D

PQ : PR = √3 : 2

12√3 : PR = √3 : 2

PR√3 = 2 × 12√3

PR = 24√3

√3

PR = 24 cm ✔

14. A

C(10, 240°)

x = 10 cos 240°

x = 10 × (–½)

x = – 5

y = 10 sin 240°

x = 10 × (–½√3)

x = – 5√3

C (–5, –5√3) ✔

15. C

A(–4, 2√2)

r = √(–4)²+(2√2)²

r = √(16 + 8)

r = √24

r = 2√6

Tan A = 2√2

–4

Tan A = –½√2

A = (180 – 35°)

A = 145°

A(2√6, 145°) ✔

16. C

sudut A = 180° – (75° + 60°)

sudut A = 180° – 135°

sudut A = 45°

12 = BC

sin 60° sin 45°

12 = BC

½√3 ½√2

12 = BC

√3 √2

BC√3 = 12√2

BC = (12√2)√3

3

BC = 4√6 cm ✔

17. A

c = √(a² + b²)

c = √(4² + 3²)

c = √25

c = 5 cm

sin A = a

c

sin A = 4 ✔

5

18. A

sin ∅ + cos ∅ = 5

sin ∅ – cos ∅

sin ∅ + cos ∅ = 5(sin ∅ – cos ∅)

sin ∅ + cos ∅ = 5sin ∅ – 5cos ∅)

sin ∅ – 5 sin ∅ = – cos ∅ – 5 cos ∅

–4 sin ∅ = –6 cos ∅

sin ∅ = –6

cos ∅ –4

tan ∅ = 3 ✔

2