Nilai dari 2sin30∘×cos120∘sin60∘×cos210∘×tan330∘=...

Pertanyaan

Nilai dari $fraction numerator sin space 60 degree cross times cos space 210 degree cross times tan space 330 degree over denominator 2 space sin space 30 degree cross times cos space 120 degree end fraction equals$ ....

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Dengan menerapkan rumus sudut-sudut berelasi dan nilai sudut istimewa, diperoleh perhitungan sebagai berikut.

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator sin space 60 degree cross times cos space 210 degree cross times tan space 330 degree over denominator 2 space sin space 30 degree cross times cos space 120 degree end fraction end cell row blank equals cell fraction numerator sin space 60 degree cross times cos space open parentheses 180 degree plus 30 degree close parentheses cross times tan space open parentheses 360 degree minus 30 degree close parentheses over denominator 2 space sin space 30 degree cross times cos space open parentheses 180 degree minus 60 degree close parentheses end fraction end cell row blank equals cell fraction numerator sin space 60 degree cross times open parentheses negative cos space 30 degree close parentheses cross times open parentheses negative tan space 30 degree close parentheses over denominator 2 space sin space 30 degree cross times open parentheses negative cos space 60 degree close parentheses end fraction end cell row blank equals cell fraction numerator up diagonal strike begin display style 1 half end style end strike square root of 3 cross times open parentheses negative up diagonal strike begin display style 1 half end style end strike square root of 3 close parentheses cross times open parentheses negative begin display style 1 third end style square root of 3 close parentheses over denominator 2 cross times up diagonal strike begin display style 1 half end style end strike cross times open parentheses negative up diagonal strike begin display style 1 half end style end strike close parentheses end fraction end cell row blank equals cell fraction numerator negative begin display style 1 third end style open parentheses 3 close parentheses over denominator negative 2 end fraction end cell row blank equals cell fraction numerator negative 1 over denominator negative 2 end fraction end cell row blank equals cell 1 half end cell end table end style$

Jadi, nilai dari $fraction numerator sin space 60 degree cross times cos space 210 degree cross times tan space 330 degree over denominator 2 space sin space 30 degree cross times cos space 120 degree end fraction$ adalah 1 half .

Dengan demikian, jawaban yang tepat adalah B.