Nomor 5
cos (–610°)
- Identitas pertama: cos (–α) = cos α
⇒ cos (–610°) = cos 610°
- Identitas kedua: cos (360°·k + α) = cos α
⇒ cos 610° = cos (360°·1 + 250°)
⇒ cos 610° = cos 250°
⇒ cos (–610°) = cos 250°
- Identitas ketiga: cos (180° + α) = –cos α
⇒ cos 250° = cos (180° + 70°)
⇒ cos 250° = –cos 70°
⇒ cos (–610°) = –cos 70°
KESIMPULAN
cos (–610°) = –cos 70°
[opsi E]
Nomor 6
sin 120° cos 60°
Cara pertama
- Identitas: sin (180° – α) = sin α
⇒ sin 120° cos 60° = sin (180° – 60°) cos 60°
⇒ sin 120° cos 60° = sin 60° cos 60°
- sin 60° = ½√3, cos 60° = ½
⇒ sin 60° cos 60° = ½√3 · ½ = ¼√3
⇒ sin 120° cos 60° = ¼√3
Cara kedua
- Identitas: sin α cos β = ½ [ sin (α+β) + sin (α–β) ]
⇒ sin 120° cos 60° = ½ [ sin (120°+60°) + sin (120°–60°) ]
⇒ sin 120° cos 60° = ½ [ sin 180° + sin 60° ]
⇒ sin 120° cos 60° = ½ [ 0 + ½√3 ]
⇒ sin 120° cos 60° = ¼√3
KESIMPULAN
sin 120° cos 60° = ¼√3
[opsi A]
Nomor 7
tan 240° – tan 210°
- Identitas: tan (180° + α) = tan α
⇒ tan 240° – tan 210° = tan (180° + 60°) – tan (180° + 30°)
⇒ tan 240° – tan 210° = tan 60° – tan 30°
⇒ tan 240° – tan 210° = √3 – (1/3)√3
⇒ tan 240° – tan 210° = (1 – 1/3)√3
⇒ tan 240° – tan 210° = (2/3)√3
KESIMPULAN
tan 240° – tan 210° = (2/3)√3
[opsi D]
Nomor 8
sin 600° + sec 660° – cot 690°
= sin (720° – 120°) + sec (720° – 60°) – cot (720° – 30°)
= sin (360°·2 – 120°) + sec (360°·2 – 60°) – cot (360°·2 – 30°)
- sin (360°·k – α) = –sin α
- sec (360°·k – α) = sec α
- cot (360°·k – α) = –cot α
= –sin 120° + sec 60° – (–cot 30°)
= sec 60° – sin 120° + cot 30°
= sec 60° – sin (180° – 60°) + cot 30°
- sin (180° – α) = sin α
= sec 60° – sin 60° + cot 30°
= (1/cos 60°) – sin 60° + (1/tan 30°)
= (1/½) – ½√3 + [1 / [(1/3)√3]]
= 2 – ½√3 + (3/√3)
= 2 – ½√3 + √3
= 2 + √3(1 – ½)
= 2 + ½√3
= ½√3 + 2
KESIMPULAN
sin 600° + sec 660° – cot 690° = ½√3 + 2
[opsi D]
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