Pertanyaan

Nilai dari sec 3 0 ∘ − cot 3 0 ∘ 2 cos 3 0 ∘ + 3 4 sin 6 0 ∘ + tan 6 0 ∘ = ...

Nilai dari $\frac{2 cos 3 0 ^{\circ} + \frac{4}{3} sin 6 0 ^{\circ} + tan 6 0 ^{\circ}}{sec 3 0 ^{\circ} - cot 3 0 ^{\circ}} =$ ...

F. Faiz

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Ingatlah perbandingan sisi (trigonometri), yaitu: Sehingga diperoleh nilai sudut trigonometrinya yaitu: Nilai dari . Jadi, jawaban yang tepat adalah D.

Ingatlah perbandingan sisi (trigonometri), yaitu:

$table attributes columnalign right center left columnspacing 0px end attributes row cell sec space straight alpha end cell equals cell fraction numerator 1 over denominator cos space straight alpha end fraction end cell row cell cot space straight alpha end cell equals cell fraction numerator 1 over denominator tan space straight alpha end fraction end cell end table$

Sehingga diperoleh nilai sudut trigonometrinya yaitu:

$fraction numerator 2 space cos space 30 degree plus begin display style 4 over 3 end style space sin space 60 degree plus tan space 60 degree over denominator sec space 30 degree minus cot space 30 degree end fraction equals fraction numerator down diagonal strike 2 times begin display style fraction numerator 1 over denominator down diagonal strike 2 end fraction end style square root of 3 plus begin display style 4 over 3 end style times begin display style 1 half end style square root of 3 plus square root of 3 over denominator begin display style fraction numerator 1 over denominator cos space 30 degree end fraction end style minus begin display style fraction numerator 1 over denominator tan space 30 degree end fraction end style end fraction equals fraction numerator square root of 3 plus begin display style 2 over 3 end style square root of 3 plus square root of 3 over denominator begin display style fraction numerator 1 over denominator begin display style 1 half end style square root of 3 end fraction end style minus begin display style fraction numerator 1 over denominator begin display style 1 third end style square root of 3 end fraction end style end fraction equals fraction numerator begin display style 3 over 3 end style square root of 3 plus begin display style 2 over 3 end style square root of 3 plus begin display style 3 over 3 end style square root of 3 over denominator begin display style fraction numerator 2 over denominator square root of 3 end fraction end style minus begin display style fraction numerator 3 over denominator square root of 3 end fraction end style end fraction equals fraction numerator begin display style 8 over 3 end style square root of 3 over denominator negative begin display style fraction numerator 1 over denominator square root of 3 end fraction end style end fraction equals 8 over 3 square root of 3 times open parentheses negative square root of 3 close parentheses equals negative 8 over 3 times square root of 3 times 3 end root equals negative fraction numerator 8 over denominator down diagonal strike 3 end fraction times down diagonal strike 3 equals negative 8$

Nilai dari $fraction numerator 2 space cos space 30 degree plus begin display style 4 over 3 end style space sin space 60 degree plus tan space 60 degree over denominator sec space 30 degree minus cot space 30 degree end fraction equals$ negative 8 .

Jadi, jawaban yang tepat adalah D.