Pembahasan soal trigonometri (7)


Soal 1
Hitung tanpa kalkulator, nilai dari 8.\sin 70^{o}.\sin 50^{o}.\sin 10^{o}.

jawab.

8.\sin 70^{o}.\sin 50^{o}.\sin 10^{o}.
= 8.(-\frac{1}{2}\cos 120^{o}+\frac{1}{2}\cos 20^{o}).\sin 10^{o}
= 8.(-\frac{1}{2}.-\frac{1}{2}+\frac{1}{2}\cos 20^{o}).\sin 10^{o}
= (2+4 \cos 20^{o}).\sin 10^{o}
= 2.\sin 10^{o}+4 \cos 20^{o}.\sin 10^{o}
= 2.\sin 10^{o}+2.2 \cos 20^{o}.\sin 10^{o}
= 2.\sin 10^{o}+2.( \sin 30^{o}-\sin 10^{o})
= 2.\sin 10^{o}+2. \sin 30^{o}- 2.\sin 10^{o}
= 2.\frac {1}{2}= 1

soal nomor 2

Hitung tanpa kalkulator nilai dari 8.\sin 20^{o}.\sin 40^{o}.\sin 80^{o}.

Jawab.

8.\sin 20^{o}.(-\frac{1}{2}\cos 120^{o}+\frac{1}{2}\cos 40^{o})
= 8.\sin 20^{o}.(-\frac{1}{2}.-\frac{1}{2}+\frac{1}{2}\cos 40^{o})
= 2.\sin 20^{o}+4.\sin 20^{o}\cos 40^{o}
= 2.\sin 20^{o}+2.2.\cos 40^{o}\sin 20^{o}
= 2.\sin 20^{o}+2.(\sin 60^{o}-\sin 20^{o})
= 2.\sin 20^{o}+2.\sin 60^{o}-2.\sin 20^{o}
=  2.\sin 60^{o}=2.\frac{1}{2}\sqrt{3}=\sqrt{3}

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