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Nilai dari sin75∘−cos15∘sin105∘+sin15∘​= ...

Pertanyaan

Nilai dari fraction numerator sin space 105 degree plus sin space 15 degree over denominator sin space 75 degree minus cos space 15 degree end fraction equals ...

Pembahasan Soal:

Perbandingan trigonometri sudut-sudut berelasi yaitu:

table row cell sin space open parentheses 90 degree minus alpha close parentheses end cell equals cell cos space alpha end cell row cell sin space open parentheses 90 degree plus alpha close parentheses end cell equals cell cos space alpha end cell end table

Sehingga diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 105 degree end cell equals cell cos space open parentheses 90 degree plus 15 degree close parentheses end cell row blank equals cell cos space 15 degree end cell row blank equals cell cos space open parentheses 45 degree minus 30 degree close parentheses end cell row blank equals cell cos space 45 degree times cos space 30 times plus sin space 45 degree times sin space 30 degree end cell row blank equals cell 1 half square root of 2 times 1 half square root of 3 plus 1 half square root of 2 times 1 half end cell row blank equals cell 1 fourth square root of 6 plus 1 fourth square root of 2 end cell row blank blank blank row cell sin space 15 degree end cell equals cell sin space open parentheses 45 degree minus 30 degree close parentheses end cell row blank equals cell sin space 45 degree times cos space 30 times negative cos space 45 degree times sin space 30 degree end cell row blank equals cell 1 half square root of 2 times 1 half square root of 3 minus 1 half square root of 2 times 1 half end cell row blank equals cell 1 fourth square root of 6 minus 1 fourth square root of 2 end cell row blank blank blank row cell sin space 75 degree end cell equals cell sin space open parentheses 90 degree minus 15 degree close parentheses end cell row blank equals cell cos space 15 degree end cell row blank equals cell cos space open parentheses 45 degree minus 30 degree close parentheses end cell row blank equals cell cos space 45 degree times cos space 30 times plus sin space 45 degree times sin space 30 degree end cell row blank equals cell 1 half square root of 2 times 1 half square root of 3 plus 1 half square root of 2 times 1 half end cell row blank equals cell 1 fourth square root of 6 plus 1 fourth square root of 2 end cell row blank blank blank row cell cos space 15 degree end cell equals cell cos space open parentheses 45 degree minus 30 degree close parentheses end cell row blank equals cell cos space 45 degree times cos space 30 times plus sin space 45 degree times sin space 30 degree end cell row blank equals cell 1 half square root of 2 times 1 half square root of 3 plus 1 half square root of 2 times 1 half end cell row blank equals cell 1 fourth square root of 6 plus 1 fourth square root of 2 end cell end table

Nilai sudut trigonometrinya yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sin space 105 degree plus sin space 15 degree over denominator sin space 75 degree minus cos space 15 degree end fraction end cell equals cell fraction numerator open parentheses begin display style 1 fourth end style square root of 6 plus begin display style 1 fourth end style square root of 2 close parentheses plus open parentheses begin display style 1 fourth end style square root of 6 minus begin display style 1 fourth end style square root of 2 close parentheses over denominator open parentheses begin display style 1 fourth end style square root of 6 plus begin display style 1 fourth end style square root of 2 close parentheses minus open parentheses begin display style 1 fourth end style square root of 6 plus begin display style 1 fourth end style square root of 2 close parentheses end fraction end cell row blank equals cell fraction numerator begin display style 1 fourth end style square root of 6 plus begin display style 1 fourth end style square root of 6 plus begin display style 1 fourth end style square root of 2 minus begin display style 1 fourth end style square root of 2 over denominator begin display style 1 fourth end style square root of 6 minus begin display style 1 fourth end style square root of 6 plus begin display style 1 fourth end style square root of 2 minus begin display style 1 fourth end style square root of 2 end fraction end cell row blank equals cell fraction numerator begin display style 2 over 4 end style square root of 6 over denominator 0 end fraction end cell row blank equals infinity end table

Maka, nilai dari fraction numerator sin space 105 degree plus sin space 15 degree over denominator sin space 75 degree minus cos space 15 degree end fraction equals infinity.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

S. Ayu

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Terakhir diupdate 06 Oktober 2021

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