Tentukan 5 nilai perbandingan trigonometri yang lain untuk setiap pernyataan berikut ini   tan α=1, π<α<23π​

Pertanyaan

Tentukan  nilai perbandingan trigonometri yang lain untuk setiap pernyataan berikut ini 

 

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F. Ayudhita

Master Teacher

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Pembahasan

Pembahasan

Ingat begin mathsize 14px style straight pi less than straight alpha less than fraction numerator 3 straight pi over denominator 2 end fraction end style, sudut berada di kuadran III begin mathsize 14px style open parentheses x less than 0 space dan space y less than 0 close parentheses end style

begin mathsize 14px style tan space straight alpha equals 1 equals fraction numerator negative 1 over denominator negative 1 end fraction equals y over x end style

Mencari nilai begin mathsize 14px style r end style:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row r equals cell square root of x squared plus y squared end root end cell row blank equals cell square root of left parenthesis negative 1 right parenthesis squared plus left parenthesis negative 1 right parenthesis squared end root end cell row blank equals cell square root of 1 plus 1 end root end cell row blank equals cell square root of 2 end cell end table end style

Jadi

  • begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank alpha end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell y over r end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator negative 1 over denominator square root of 2 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cross times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 2 over denominator square root of 2 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 half end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 2 end cell end table end style
  • begin mathsize 14px style cos space alpha equals x over r equals fraction numerator negative 1 over denominator square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction equals negative 1 half square root of 2 end style
  • begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cot end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank alpha end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell x over y end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator negative 1 over denominator negative 1 end fraction end cell equals 1 end table end style
  • begin mathsize 14px style cos e c space table attributes columnalign right center left columnspacing 0px end attributes row blank blank alpha end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell r over y end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator square root of 2 over denominator negative 1 end fraction end cell equals cell negative square root of 2 end cell end table end style
  • begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank sec end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank alpha end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell r over x end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator square root of 2 over denominator negative 1 end fraction end cell equals cell negative square root of 2 end cell end table end style

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Rafita Salsabila

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Tentukan 5 nilai perbandingan trigonometri yang lain untuk setiap pernyataan berikut ini   cos α=53​, 23π​<α<2π

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