Pertanyaan

Tentukannilai perbandingan trigonometri yang lain untuk setiap pernyataan berikut ini. sec β = − 2 , π < β < 2 3 π

Tentukan nilai perbandingan trigonometri yang lain untuk setiap pernyataan berikut ini.

$sec β = - 2$ , $π < β < \frac{3 π}{2}$

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Pembahasan

Ingat , sudut berada di kuadran III Mencari nilai : Jadi

Ingat $begin mathsize 14px style straight pi less than straight beta less than fraction numerator 3 straight pi over denominator 2 end fraction end style$ , sudut berada di kuadran III

$begin mathsize 14px style sec space straight beta equals fraction numerator 2 over denominator negative 1 end fraction equals r over x end style$

Mencari nilai :

Jadi

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank beta end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell y over r end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator negative square root of 3 over denominator 2 end fraction end cell equals cell negative 1 half square root of 3 end cell end table end style$
$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank beta end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell x over r end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator negative 1 over denominator 2 end fraction end cell end table equals negative 1 half end style$
$begin mathsize 14px style tan space beta table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell y over x end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator negative square root of 3 over denominator negative 1 end fraction end cell equals cell square root of 3 end cell end table end style$
$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank co end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank tan end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table beta table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell x over y end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator negative 1 over denominator negative square root of 3 end fraction cross times fraction numerator square root of 3 over denominator square root of 3 end fraction end cell equals cell 1 third square root of 3 end cell end table end style$
$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank ec end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank beta end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell r over y end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 over denominator negative square root of 3 end fraction cross times fraction numerator square root of 3 over denominator square root of 3 end fraction end cell equals cell negative 2 over 3 square root of 3 end cell end table end style$

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