Pertanyaan

Diketahui sec C = 3 ​ dan 27 0 ∘ < C < 36 0 ∘ . Nilai tan C = ...

Diketahui  dan . Nilai  

  1. begin mathsize 14px style... end style    

  2. begin mathsize 14px style... end style  

A. Armanda

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

Jawaban terverifikasi

Pembahasan

karena dan , dengan menggunakan teorema Pythagoras: karena pada kuadran IV tangen bernilai negatif, maka pilih . Sehingga, Jadi, .

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos space straight C end cell equals cell samping over miring end cell row cell sec space straight C end cell equals cell fraction numerator 1 over denominator cos space straight C end fraction end cell row cell fraction numerator square root of 3 over denominator 1 end fraction end cell equals cell miring over samping end cell end table end style  

karena begin mathsize 14px style miring equals square root of 3 end style dan size 14px samping size 14px equals size 14px 1, dengan menggunakan teorema Pythagoras:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell miring squared end cell equals cell depan squared plus samping squared end cell row cell open parentheses square root of 3 close parentheses squared end cell equals cell depan squared plus 1 squared end cell row depan equals cell plus-or-minus square root of open parentheses square root of 3 close parentheses squared minus 1 squared end root end cell row blank equals cell plus-or-minus square root of 3 minus 1 end root end cell row blank equals cell plus-or-minus square root of 2 end cell end table end style 

karena pada kuadran IV begin mathsize 14px style open parentheses 270 degree less than straight C less than 360 degree close parentheses end style tangen bernilai negatif, maka pilih begin mathsize 14px style depan table attributes columnalign right center left columnspacing 0px end attributes row blank equals minus 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. Sehingga,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan space straight C end cell equals cell de over sa end cell row blank equals cell fraction numerator negative square root of 2 over denominator 1 end fraction end cell row blank equals cell negative 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 tan 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 straight C end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals minus 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.

 

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Diketahui tanx = b dengan 18 0 ∘ < x < 27 0 ∘ . Tentukan nilai sec x

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