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Persamaan garis normal pada kurva  di titik yang berabsis  adalah ...

Pertanyaan

Persamaan garis normal pada kurva y equals fraction numerator cos space x over denominator 1 plus sin space x end fraction di titik yang berabsis x equals straight pi over 2 adalah ...

  1. y equals 2 open parentheses x minus straight pi over 2 close parentheses 

  2. y equals negative open parentheses x minus straight pi over 2 close parentheses 

  3. y equals negative 1 half open parentheses x minus straight pi over 2 close parentheses 

  4. y equals open parentheses x minus straight pi over 2 close parentheses 

  5. y equals 1 half open parentheses x minus straight pi over 2 close parentheses 

Pembahasan Soal:

Mencari turunan fungsi:

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell fraction numerator cos space x over denominator 1 plus sin space x end fraction end cell row cell y apostrophe end cell equals cell fraction numerator straight d over denominator straight d x end fraction left parenthesis y right parenthesis end cell row blank equals cell fraction numerator straight d over denominator straight d x end fraction open parentheses fraction numerator cos space x over denominator 1 plus sin space x end fraction close parentheses end cell row blank equals cell fraction numerator fraction numerator straight d over denominator straight d x end fraction open parentheses cos open parentheses x close parentheses close parentheses open parentheses 1 plus sin open parentheses x close parentheses close parentheses minus fraction numerator straight d over denominator straight d x end fraction open parentheses 1 plus sin open parentheses x close parentheses close parentheses cos open parentheses x close parentheses over denominator open parentheses 1 plus sin open parentheses x close parentheses close parentheses squared end fraction end cell row blank equals cell fraction numerator open parentheses negative sin open parentheses x close parentheses close parentheses open parentheses 1 plus sin open parentheses x close parentheses close parentheses minus cos open parentheses x close parentheses cos open parentheses x close parentheses over denominator open parentheses 1 plus sin open parentheses x close parentheses close parentheses squared end fraction end cell row blank equals cell fraction numerator negative sin open parentheses x close parentheses open parentheses sin open parentheses x close parentheses plus 1 close parentheses minus cos squared open parentheses x close parentheses over denominator open parentheses 1 plus sin open parentheses x close parentheses close parentheses squared end fraction end cell row blank equals cell negative fraction numerator 1 over denominator 1 plus sin open parentheses x close parentheses end fraction end cell end table 

Substitusi nilai x equals straight pi over 2 ke turunan fungsi:

table attributes columnalign right center left columnspacing 0px end attributes row cell negative fraction numerator 1 over denominator 1 plus sin open parentheses x close parentheses end fraction end cell equals cell negative fraction numerator 1 over denominator 1 plus sin open parentheses 180 over 2 close parentheses end fraction end cell row blank equals cell negative fraction numerator 1 over denominator 1 plus sin open parentheses 90 close parentheses end fraction end cell row blank equals cell negative fraction numerator 1 over denominator 1 plus 1 end fraction end cell row blank equals cell negative 1 half end cell end table 

Didapat gradiennya adalah negative 1 half.

Gradien garis normal:

straight m space normal equals negative 1 over straight m equals negative fraction numerator 1 over denominator negative begin display style 1 half end style end fraction equals 2 

Substitusi nilai x equals straight pi over 2 ke y equals fraction numerator cos space x over denominator 1 plus sin space x end fraction.

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell fraction numerator cos space x over denominator 1 plus sin space x end fraction end cell row blank equals cell fraction numerator cos open parentheses 90 degree close parentheses over denominator 1 plus sin open parentheses 90 degree close parentheses end fraction end cell row blank equals cell fraction numerator 0 over denominator 1 plus 1 end fraction end cell row blank equals 0 end table 

Maka persamaan garis normalnya adalah 

table attributes columnalign right center left columnspacing 0px end attributes row cell y minus y subscript 1 end cell equals cell m open parentheses x minus x subscript 1 close parentheses end cell row cell y minus 0 end cell equals cell 2 open parentheses x minus straight pi over 2 close parentheses end cell row y equals cell 2 open parentheses x minus straight pi over 2 close parentheses end cell end table 

Jadi, persamaan garis normalnya adalah y equals 2 open parentheses x minus straight pi over 2 close parentheses.

Dengan demikian, jawaban  yang tepat adalah A.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 02 Juni 2021

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