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Pertanyaan

Nilai dari fraction numerator sin space 150 to the power of degree plus sin space 120 to the power of degree over denominator cos space 210 to the power of degree minus cos space 300 to the power of degree end fraction equals...

  1. 2

  2. 1

  3. 0

  4. negative 1 half

  5. negative 1

M. Nasrullah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

jawabannya adalah E

Pembahasan

Ingat bahwa:

sin space open parentheses 180 minus alpha close parentheses equals sin space alpha

cos space open parentheses 360 minus alpha close parentheses equals cos space alpha

cos space open parentheses 180 plus alpha close parentheses equals negative cos space alpha

Sehingga diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 150 to the power of degree end cell equals cell sin space left parenthesis 180 minus 30 right parenthesis end cell row blank equals cell sin space 30 end cell row blank equals cell 1 half end cell row cell sin space 120 to the power of degree end cell equals cell sin space left parenthesis 180 minus 60 right parenthesis end cell row blank equals cell sin space 60 end cell row blank equals cell 1 half square root of 3 end cell row cell cos space 210 to the power of degree end cell equals cell cos space left parenthesis 180 plus 30 right parenthesis end cell row blank equals cell negative cos space 30 end cell row blank equals cell negative 1 half square root of 3 end cell row cell cos space 300 to the power of degree end cell equals cell cos space left parenthesis 360 minus 60 right parenthesis end cell row blank equals cell cos space 60 end cell row blank equals cell 1 half end cell end table 

Setelah mendapatkan hasilnya subsitusikan 

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sin space 150 to the power of degree plus sin space 120 to the power of degree over denominator cos space 210 to the power of degree minus cos space 300 to the power of degree end fraction end cell equals cell fraction numerator begin display style 1 half end style plus begin display style 1 half end style square root of 3 over denominator negative begin display style 1 half end style square root of 3 minus begin display style 1 half end style end fraction end cell row blank equals cell fraction numerator begin display style 1 half end style left parenthesis 1 plus square root of 3 right parenthesis over denominator negative begin display style 1 half end style left parenthesis 1 plus square root of 3 right parenthesis end root end fraction end cell row blank equals cell negative 1 end cell end table

Oleh karena itu jawabannya adalah E

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