Pertanyaan

Nilai cos 7 2 π + cos 7 4 π + cos 7 6 π = ...

Nilai $cos \frac{2 π}{7} + cos \frac{4 π}{7} + cos \frac{6 π}{7} = ...$

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A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

$begin mathsize 12px style open parentheses cos fraction numerator 2 straight pi over denominator 7 end fraction plus cos fraction numerator begin display style 4 straight pi end style over denominator begin display style 7 end style end fraction plus cos fraction numerator begin display style 6 straight pi end style over denominator begin display style 7 end style end fraction close parentheses times fraction numerator sin begin display style straight pi over 7 end style over denominator sin straight pi over 7 end fraction equals fraction numerator cos fraction numerator 2 straight pi over denominator 7 end fraction times sin straight pi over 7 plus cos fraction numerator begin display style 4 straight pi end style over denominator begin display style 7 end style end fraction times sin straight pi over 7 plus cos fraction numerator begin display style 6 straight pi end style over denominator begin display style 7 end style end fraction times sin straight pi over 7 over denominator sin straight pi over 7 end fraction Ingat space rumus colon 2 space cos space A space sin space B equals sin open parentheses A plus B close parentheses minus sin open parentheses A minus B close parentheses cos space A space sin space B equals 1 half sin open parentheses A plus B close parentheses minus sin open parentheses A minus B close parentheses maka colon fraction numerator begin display style 1 half end style open parentheses sin begin display style fraction numerator 3 straight pi over denominator 7 end fraction end style minus sin straight pi over 7 close parentheses plus 1 half open parentheses sin fraction numerator 5 straight pi over denominator 7 end fraction minus sin fraction numerator 3 straight pi over denominator 7 end fraction close parentheses plus 1 half open parentheses sin straight pi minus sin fraction numerator 5 straight pi over denominator 7 end fraction close parentheses over denominator sin straight pi over 7 end fraction equals fraction numerator begin display style sin fraction numerator 3 straight pi over denominator 7 end fraction minus sin straight pi over 7 plus sin fraction numerator 5 straight pi over denominator 7 end fraction minus sin fraction numerator 3 straight pi over denominator 7 end fraction plus sinπ minus sin fraction numerator 5 straight pi over denominator 7 end fraction end style over denominator 2 space sin straight pi over 7 end fraction equals fraction numerator begin display style sin fraction numerator 3 straight pi over denominator 7 end fraction minus sin straight pi over 7 plus sin fraction numerator 5 straight pi over denominator 7 end fraction minus sin fraction numerator 3 straight pi over denominator 7 end fraction plus sinπ minus sin fraction numerator 5 straight pi over denominator 7 end fraction end style over denominator 2 space sin straight pi over 7 end fraction equals fraction numerator begin display style sinπ minus sin straight pi over 7 end style over denominator 2 space sin straight pi over 7 end fraction equals fraction numerator begin display style 0 minus sin straight pi over 7 end style over denominator 2 space sin straight pi over 7 end fraction equals fraction numerator begin display style negative sin straight pi over 7 end style over denominator 2 space sin straight pi over 7 end fraction equals negative 1 half end style$