Pertanyaan

Jika nilai f ( a ) = 9 − π untuk fungsi f ( x ) = c osec 3 π x + sec 6 π x , maka nilai adalah...

Jika nilai $f (a) = \frac{- π}{9}$ untuk fungsi $f (x) = c osec \frac{π}{3} x + sec \frac{π}{6} x$ , maka nilai $a$ adalah...

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Habis dalam

Klaim

G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah E.

Pembahasan

Cari turunan dari Di dapatkan . Karena pada soal maka : Jadi, nilai . Oleh karena itu, jawaban yang benar adalah E.

Cari turunan dari f left parenthesis x right parenthesis equals c osec straight pi over 3 straight x plus sec straight pi over 6 straight x

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f plus-or-minus g close parentheses apostrophe end cell equals cell f thin space apostrophe plus-or-minus g apostrophe end cell row cell fraction numerator d over denominator d x end fraction open parentheses csc open parentheses pi over 3 close parentheses x plus sec open parentheses pi over 6 close parentheses x close parentheses end cell equals cell fraction numerator d over denominator d x end fraction open parentheses csc open parentheses pi over 3 close parentheses x close parentheses plus fraction numerator d over denominator d x end fraction open parentheses sec open parentheses pi over 6 close parentheses x close parentheses end cell row blank equals cell csc open parentheses pi over 3 close parentheses fraction numerator d over denominator d x end fraction open parentheses x close parentheses plus sec open parentheses pi over 6 close parentheses fraction numerator d over denominator d x end fraction open parentheses x close parentheses end cell row blank equals cell csc open parentheses pi over 3 close parentheses times thin space 1 plus sec open parentheses pi over 6 close parentheses times thin space 1 end cell row blank equals cell 1 times fraction numerator 2 square root of 3 over denominator 3 end fraction plus 1 times fraction numerator 2 square root of 3 over denominator 3 end fraction end cell row blank equals cell fraction numerator 2 over denominator square root of 3 end fraction plus fraction numerator 2 over denominator square root of 3 end fraction end cell row blank equals cell fraction numerator 4 over denominator square root of 3 end fraction end cell end table end style$

Di dapatkan $f apostrophe left parenthesis x right parenthesis equals fraction numerator 4 over denominator square root of 3 end fraction$ . Karena pada soal $f apostrophe left parenthesis a right parenthesis equals fraction numerator negative straight pi over denominator 9 end fraction$ maka :

$table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis a right parenthesis end cell equals cell fraction numerator negative straight pi over denominator 9 end fraction end cell row cell 4 over 3 square root of 3 end cell equals cell fraction numerator negative straight pi over denominator 9 end fraction end cell row cell 4 over 3 square root of 3 times 9 end cell equals cell negative straight pi end cell row cell 36 over 3 end cell equals cell negative straight pi end cell row 12 equals cell negative straight pi end cell row 6 equals cell negative straight pi over 2 end cell end table$

Jadi, nilai a equals 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 straight pi over 2 end cell end table .

Oleh karena itu, jawaban yang benar adalah E.