Pertanyaan

Jika f ( x ) = sin x sin x − cos x , f ( 3 1 π ) = ...

Jika $f (x) = \frac{sin x - cos x}{sin x}$ , $f (\frac{1}{3} π) = ...$

G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Cari dulu turunan dari , Kemudian subtitusi ke dalam fungsi, Oleh karena itu, jawaban yang benar adalah D.

table attributes columnalign right center left columnspacing 0px end attributes row straight pi equals 180 row cell f apostrophe open parentheses 1 third straight pi close parentheses end cell equals cell f apostrophe open parentheses 1 third cross times 180 close parentheses end cell row blank equals cell f apostrophe open parentheses 60 close parentheses end cell end table

Cari dulu turunan dari $f left parenthesis x right parenthesis equals fraction numerator sin space x minus cos space x over denominator sin space x end fraction$ ,

$table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell u over v end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator u apostrophe v minus u v apostrophe over denominator v squared end fraction end cell row u equals cell sin space x minus cos space x end cell row v equals cell sin space x end cell row cell u apostrophe end cell equals cell cos x minus left parenthesis negative sin x right parenthesis end cell row cell u apostrophe end cell equals cell cos space x plus sin space x end cell row cell v apostrophe end cell equals cell co s space x end cell row blank blank blank row cell f left parenthesis x right parenthesis end cell equals cell fraction numerator sin space x minus cos space x over denominator sin space x end fraction end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator open parentheses cos space x plus sin space x close parentheses sin space x minus open parentheses sin space x minus cos space x close parentheses co s space x over denominator open parentheses sin space x close parentheses squared end fraction end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator up diagonal strike sin space x space cos space x end strike space plus sin squared x up diagonal strike negative sin space x space cos space x end strike plus cos squared x over denominator sin squared x end fraction end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator sin squared x plus cos squared x over denominator sin squared x end fraction end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator 1 over denominator sin squared x end fraction end cell row blank blank blank row blank blank blank end table$

Kemudian subtitusi x equals 60 degree ke dalam fungsi,

$table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator 1 over denominator sin squared x end fraction end cell row cell f apostrophe left parenthesis 60 right parenthesis end cell equals cell 1 over open parentheses sin space 60 close parentheses squared end cell row cell f apostrophe left parenthesis 60 right parenthesis end cell equals cell 1 over open parentheses begin display style 1 half end style square root of 3 close parentheses squared end cell row cell f apostrophe left parenthesis 60 right parenthesis end cell equals cell fraction numerator 1 over denominator open parentheses begin display style 1 fourth cross times 3 end style close parentheses end fraction end cell row cell f apostrophe left parenthesis 60 right parenthesis end cell equals cell fraction numerator 1 over denominator open parentheses begin display style 3 over 4 end style close parentheses end fraction end cell row cell f apostrophe left parenthesis 60 right parenthesis end cell equals cell 1 divided by 3 over 4 end cell row cell f apostrophe left parenthesis 60 right parenthesis end cell equals cell 1 cross times 4 over 3 end cell row cell f apostrophe left parenthesis 60 right parenthesis end cell equals cell 4 over 3 end cell row cell f apostrophe left parenthesis 60 right parenthesis end cell equals cell 1 1 third end cell row blank blank blank end table$

Oleh karena itu, jawaban yang benar adalah D.