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Pertanyaan

Nilai dari begin mathsize 14px style fraction numerator open parentheses sin begin display style straight pi over 3 end style plus cos begin display style straight pi over 6 end style close parentheses over denominator open parentheses tan begin display style straight pi over 3 end style plus c o t begin display style straight pi over 6 end style close parentheses end fraction end style adalah ....

  1. begin mathsize 14px style fraction numerator open parentheses 3 plus square root of 6 close parentheses over denominator 12 end fraction end style 

  2. begin mathsize 14px style 2 end style 

  3. begin mathsize 14px style 0 end style 

  4. begin mathsize 14px style 1 half end style 

  5. begin mathsize 14px style fraction numerator square root of 2 over denominator 2 end fraction end style 

F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Nilai dari begin mathsize 14px style straight pi over 3 equals 60 degree space dan space straight pi over 6 equals 30 degree end style, Nilai trigonometri sudut istimewa yaitu

begin mathsize 14px style sin space 30 degree equals 1 half semicolon space sin space 60 degree equals 1 half square root of 3 semicolon cos space 30 degree equals 1 half square root of 3 semicolon space cos space 60 degree equals 1 half end style

Ingat bahwa, begin mathsize 14px style tan space x equals fraction numerator sin space x over denominator cos space x end fraction space d a n space cot space x equals fraction numerator cos space x over denominator sin space x end fraction end style, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sin space begin display style straight pi over 3 end style plus cos space begin display style straight pi over 6 end style over denominator tan space begin display style straight pi over 3 end style plus cot space begin display style straight pi over 6 end style end fraction end cell equals cell fraction numerator sin space 60 degree plus cos space 30 degree over denominator begin display style fraction numerator sin space 60 degree over denominator cos space 60 degree end fraction end style plus begin display style fraction numerator cos space 30 degree over denominator sin space 30 degree end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style 1 half end style square root of 2 plus begin display style 1 half end style square root of 2 over denominator begin display style fraction numerator begin display style 1 half end style square root of 2 over denominator begin display style 1 half end style end fraction end style plus begin display style fraction numerator 1 half square root of 2 over denominator begin display style 1 half end style end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style square root of 2 end style over denominator begin display style square root of 2 end style end fraction cross times 2 end cell row blank equals 2 end table end style

Jadi, jawaban yang tepat adalah B.

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