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Pertanyaan

Himpunan semua bilangan real x pada selang left square bracket 0 comma space 2 straight pi right square bracket yang memenuhi 2 cos squared x less or equal than 1 minus 3 cos space 2 x berbentuk left square bracket a comma space b right square bracket space union space left square bracket c comma space d right square bracket. Nilai a plus b plus c plus d adalah ....

  1. straight pi over 2      

  2. fraction numerator 2 straight pi over denominator 6 end fraction      

  3. fraction numerator 3 straight pi over denominator 4 end fraction      

  4. fraction numerator 7 straight pi over denominator 4 end fraction      

  5. 4 straight pi      

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A. 

Pembahasan

Soal tersebut dapat diselesaikan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 cos squared x end cell less or equal than cell 1 minus 3 cos 2 x end cell row cell 2 cos squared x end cell less or equal than cell 1 minus 3 left parenthesis 2 cos squared x minus 1 right parenthesis end cell row cell 2 cos squared x end cell less or equal than cell 1 plus 3 minus 6 cos squared x end cell row cell 8 cos squared x minus 4 end cell less or equal than 0 row cell cos squared x minus 1 half end cell less or equal than 0 row cell open parentheses cos squared x minus 1 half square root of 2 close parentheses open parentheses cos squared x plus 1 half square root of 2 close parentheses end cell less or equal than 0 row cell cos space x end cell equals cell 1 half square root of 2 end cell row x equals cell straight pi over 4 space dan space x equals fraction numerator 7 straight pi over denominator 4 end fraction end cell row cell cos space x end cell equals cell negative 1 half square root of 2 end cell row x equals cell fraction numerator 3 straight pi over denominator 4 end fraction space dan space x equals fraction numerator 5 straight pi over denominator 4 end fraction end cell row cell H P end cell equals cell open square brackets straight pi over 4 comma fraction numerator 3 straight pi over denominator 4 end fraction close square brackets union open square brackets fraction numerator 5 straight pi over denominator 4 end fraction comma fraction numerator 7 straight pi over denominator 4 end fraction close square brackets end cell end table 

Sehingga didapat sebagai berikut:

a plus b plus c minus d equals straight pi over 4 plus fraction numerator 3 straight pi over denominator 4 end fraction plus fraction numerator 5 straight pi over denominator 4 end fraction minus fraction numerator 7 straight pi over denominator 4 end fraction equals straight pi over 2 

Oleh karena itu, jawaban yang tepat adalah A. 

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