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Pertanyaan

Jika fraction numerator 3 straight pi over denominator 2 end fraction less than x less than 2 straight pi dan tan space x equals k, maka nilai dari sin space x space cos space x = ....

  1. negative fraction numerator 1 over denominator k squared plus 1 end fraction 

  2. negative fraction numerator k over denominator k squared plus 1 end fraction 

  3. fraction numerator k over denominator k squared plus 1 end fraction 

  4. negative fraction numerator k over denominator k squared minus 1 end fraction 

  5. fraction numerator k over denominator k squared minus 1 end fraction 

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Ingat kembali perbandingan sisi dalam trigonometri.

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space x end cell equals cell de over mi end cell row cell cos space x end cell equals cell sa over mi end cell row cell tan space x space end cell equals cell de over sa end cell end table

fraction numerator 3 straight pi over denominator 2 end fraction less than x less than 2 straight pi berarti 270 degree less than x less than 360 degree berada di kuadran IV.

tan space x equals k over 1 equals depan over samping, maka

table attributes columnalign right center left columnspacing 0px end attributes row miring equals cell square root of de squared plus sa squared end root end cell row blank equals cell square root of k squared plus 1 squared end root end cell row blank equals cell square root of k squared plus 1 end root end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space x end cell equals cell de over mi end cell row blank equals cell fraction numerator k over denominator square root of k squared plus 1 end root end fraction end cell row cell cos space x end cell equals cell sa over mi end cell row blank equals cell fraction numerator 1 over denominator square root of k squared plus 1 end root end fraction end cell end table

Sehingga, didapat perhitungan berikut ini.

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space x space cos space x end cell equals cell fraction numerator k over denominator square root of k squared plus 1 end root end fraction times fraction numerator 1 over denominator square root of k squared plus 1 end root end fraction end cell row blank equals cell fraction numerator k over denominator k squared plus 1 end fraction end cell end table

Dengan demikian, nilai dari sin space x space cos space x adalah fraction numerator k over denominator k squared plus 1 end fraction.

Oleh karena itu, jawaban yang benar adalah C.

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Jawaban terverifikasi

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