Pertanyaan

Tentukan 5 nilai perbandingan trigonometri yang lain untuk setiap pernyataan berikut ini. csc β = − 2 2 3 , 2 3 π < β < 2 π

Tentukan $5$ nilai perbandingan trigonometri yang lain untuk setiap pernyataan berikut ini.

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

F. Ayudhita

Master Teacher

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Pembahasan

Ingat , sudut berada di kuadran IV . Mencari nilai : Jadi

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

$begin mathsize 14px style csc space straight beta equals fraction numerator 2 square root of 3 over denominator negative 2 end fraction equals r over y end style$

Mencari nilai :

Jadi

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank beta end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell y over r end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator negative 2 over denominator 2 square root of 3 end fraction cross times fraction numerator square root of 3 over denominator square root of 3 end fraction end cell equals cell negative 1 third square root of 3 end cell end table end style$
$begin mathsize 14px style cos space table attributes columnalign right center left columnspacing 0px end attributes row blank blank beta end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell x over r end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 square root of 2 over denominator 2 square root of 3 end fraction cross times fraction numerator square root of 3 over denominator square root of 3 end fraction end cell equals cell 1 third square root of 6 end cell end table end style$
$begin mathsize 14px style tan space table attributes columnalign right center left columnspacing 0px end attributes row blank blank beta end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell y over x end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator negative 2 over denominator 2 square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell equals cell negative 1 half square root of 2 end cell end table end style$
$begin mathsize 14px style cotan space table attributes columnalign right center left columnspacing 0px end attributes row blank blank beta end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell x over y end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 square root of 2 over denominator negative 2 end fraction end cell equals cell negative square root of 2 end cell end table end style$
$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank s end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank ec end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank beta end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell r over x end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 square root of 3 over denominator 2 square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell equals cell 1 half square root of 6 end cell end table end style$

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