Pertanyaan

Nilai dari ekspresi: sin 3 0 ∘ 1 ⋅ sin 4 5 ∘ 1 ⋅ sin 6 0 ∘ 1 ⋅ sin 9 0 ∘ 1 adalah ....

Nilai dari ekspresi:

$\frac{1}{sin 3 0 ^{\circ}} \cdot \frac{1}{sin 4 5 ^{\circ}} \cdot \frac{1}{sin 6 0 ^{\circ}} \cdot \frac{1}{sin 9 0 ^{\circ}}$

adalah ....

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Klaim

E. Nur

Master Teacher

Mahasiswa/Alumni Institut Teknologi Sepuluh Nopember

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Perhatikan perhitungan berikut ini! Dengan demikian hasil dari . Oleh karena itu, jawaban yang benar adalah D.

Perhatikan perhitungan berikut ini!

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 over denominator sin space 30 degree end fraction times fraction numerator 1 over denominator sin space 45 degree end fraction times fraction numerator 1 over denominator sin space 60 degree end fraction times fraction numerator 1 over denominator sin space 90 degree end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style 1 half end style end fraction times fraction numerator 1 over denominator begin display style 1 half end style square root of 2 end fraction times fraction numerator 1 over denominator begin display style 1 half end style square root of 3 end fraction times 1 over 1 end cell row blank equals cell 2 over 1 times fraction numerator 2 over denominator square root of 2 end fraction times fraction numerator 2 over denominator square root of 3 end fraction times 1 end cell row blank equals cell fraction numerator 8 over denominator square root of 6 end fraction end cell row blank equals cell fraction numerator 8 over denominator square root of 6 end fraction cross times fraction numerator square root of 6 over denominator square root of 6 end fraction end cell row blank equals cell 8 over 6 square root of 6 end cell end table$

Dengan demikian hasil dari $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 over denominator sin space 30 degree end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 over denominator sin space 45 degree end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 over denominator sin space 60 degree end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 over denominator sin space 90 degree end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 8 over 6 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 6 end cell end table$ .

Oleh karena itu, jawaban yang benar adalah D.