Jika g(x)=2sin3(3x−2π), nilai g(π)=....

Pertanyaan

Jika $g(x)=2\sin^3(3x-2\mathrm\pi)$ , nilai $g\;(\mathrm\pi)=....$

$18$
$6$
$3$
$1$
$0$

Pembahasan Soal:

Diketahui $g left parenthesis x right parenthesis equals 2 sin cubed left parenthesis 3 x minus 2 straight pi right parenthesis$ . Misal $sin left parenthesis 3 x minus 2 straight pi right parenthesis equals u rightwards arrow fraction numerator d u over denominator d x end fraction equals 3 cos left parenthesis 3 x minus 2 straight pi right parenthesis$ , sehingga

$table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis x right parenthesis end cell equals cell 2 sin cubed left parenthesis 3 x minus 2 straight pi right parenthesis end cell row blank equals cell 2 u cubed end cell row cell g apostrophe left parenthesis x right parenthesis end cell equals cell 6 u squared times fraction numerator d u over denominator d x end fraction end cell row blank equals cell 6 sin squared left parenthesis 3 x minus 2 straight pi right parenthesis times 3 cos left parenthesis 3 straight x minus 2 straight pi right parenthesis end cell row blank equals cell 18 sin squared left parenthesis 3 x minus 2 straight pi right parenthesis cos left parenthesis 3 x minus 2 straight pi right parenthesis end cell row cell g apostrophe left parenthesis straight pi right parenthesis end cell equals cell 18 sin squared left parenthesis straight pi right parenthesis cos left parenthesis straight pi right parenthesis end cell row blank equals cell 18 cross times 0 squared cross times 1 end cell row blank equals 0 end table$

Oleh karena itu, jawaban yang benar adalah E.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

F. Kurnia

Mahasiswa/Alumni Universitas Jember

Terakhir diupdate 07 Oktober 2021

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Pertanyaan yang serupa

Jika g(x)=2sin3(3x−2π), nilai g(π)=....

Pembahasan Soal:

Oleh karena itu, jawaban yang benar adalah E.

Roboguru

Diketahui f(x)=sin2(3x−π). Nilai f(2π)=....

Pembahasan Soal:

Diketahui $f left parenthesis x right parenthesis equals sin squared left parenthesis 3 x minus straight pi right parenthesis$ , Misal $u equals sin left parenthesis 3 x minus straight pi right parenthesis rightwards arrow fraction numerator d u over denominator d x end fraction equals 3 cos left parenthesis 3 x minus straight pi right parenthesis$ . Turunan pertama $f left parenthesis x right parenthesis$ yaitu

$table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell sin squared left parenthesis 3 x minus straight pi right parenthesis end cell row blank equals cell u squared end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell 2 u times fraction numerator d u over denominator d x end fraction end cell row blank equals cell 2 sin left parenthesis 3 x minus straight pi right parenthesis times 3 cos left parenthesis 3 x minus straight pi right parenthesis end cell row cell f apostrophe open parentheses straight pi over 2 close parentheses end cell equals cell 6 sin open parentheses straight pi over 2 close parentheses cos open parentheses straight pi over 2 close parentheses end cell row blank equals cell 6 cross times 0 cross times 0 end cell row blank equals 0 end table$

Oleh karena itu, jawaban yang benar adalah C.

Roboguru

Diketahui f(x)=sin2x, maka f(125π) adalah ...

Pembahasan Soal:

Ingat konsep aturan rantai pada fungsi trigonometri jika $y equals f open parentheses u close parentheses$ , $u equals g open parentheses x close parentheses$ maka:

$fraction numerator straight d y over denominator straight d x end fraction equals fraction numerator straight d y over denominator straight d u end fraction times fraction numerator straight d u over denominator straight d x end fraction$

ingat konsep pada fungsi trigonometri:

$table attributes columnalign right center left columnspacing 0px end attributes row cell 2 sin x times cos x end cell equals cell sin space 2 x end cell row cell sin space open parentheses 180 degree minus alpha close parentheses end cell equals cell sin space alpha end cell end table$

Diketahui $f open parentheses x close parentheses equals sin squared x$ , misalkan $straight u equals sin space x$ maka:

$table attributes columnalign right center left columnspacing 0px end attributes row u equals cell sin space x end cell row cell fraction numerator d u over denominator d x end fraction end cell equals cell cos space x end cell end table$

sehingga:

$table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell sin squared x end cell row cell f open parentheses x close parentheses end cell equals cell open parentheses sin space x close parentheses squared end cell row cell f open parentheses x close parentheses end cell equals cell u squared end cell row cell fraction numerator straight d f over denominator straight d x end fraction end cell equals cell fraction numerator straight d f over denominator straight d u end fraction times fraction numerator straight d u over denominator straight d x end fraction end cell row blank equals cell 2 u to the power of 2 minus 1 end exponent times cos space x end cell row blank equals cell 2 u times cos space x end cell row blank equals cell 2 sin space x times cos space x end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell sin space 2 x end cell end table$

sehingga $f apostrophe open parentheses fraction numerator 5 straight pi over denominator 12 end fraction close parentheses$ :

$table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe open parentheses x close parentheses end cell equals cell sin space 2 x end cell row cell f apostrophe open parentheses fraction numerator 5 straight pi over denominator 12 end fraction close parentheses end cell equals cell sin space 2 open parentheses fraction numerator 5 straight pi over denominator 12 end fraction close parentheses end cell row blank equals cell sin space 2 open parentheses fraction numerator 5 cross times 180 degree over denominator 12 end fraction close parentheses end cell row blank equals cell sin space 2 open parentheses 75 degree close parentheses end cell row blank equals cell sin space 150 degree end cell row blank equals cell sin space open parentheses 180 minus 30 degree close parentheses end cell row blank equals cell sin space 30 degree end cell row blank equals cell 1 half end cell end table$

Dengan demikian nilai $f apostrophe open parentheses fraction numerator 5 straight pi over denominator 12 end fraction close parentheses$ adalah $1 half$ .

Roboguru

Diketahui fungsi f(x)=sin2x dan f(x)=−1 untuk 0∘≤x≤180∘. Nilai x yang memenuhi adalah ....

Pembahasan Soal:

Diketahui $f left parenthesis x right parenthesis equals sin squared x$ dan $f apostrophe apostrophe left parenthesis x right parenthesis equals negative 1$ untuk $0 degree less or equal than x less or equal than 180 degree$

Misal $u equals sin x rightwards arrow fraction numerator d u over denominator d x end fraction equals cos x$ . Turunan pertama $f left parenthesis x right parenthesis$ yaitu

$table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell sin squared x end cell row blank equals cell u squared end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell 2 u times fraction numerator d u over denominator d x end fraction end cell row blank equals cell 2 left parenthesis sin x right parenthesis cos x end cell row blank equals cell sin left parenthesis 2 x right parenthesis end cell end table$

Misal $u equals sin 2 x rightwards arrow fraction numerator d u over denominator d x end fraction equals 2 cos 2 x$ . Turunan kedua $f left parenthesis x right parenthesis$ yaitu

$table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis x right parenthesis end cell equals cell sin left parenthesis 2 x right parenthesis end cell row cell f apostrophe apostrophe left parenthesis x right parenthesis end cell equals cell 2 cos left parenthesis 2 x right parenthesis end cell row cell negative 1 end cell equals cell 2 cos left parenthesis 2 x right parenthesis end cell row cell cos left parenthesis 2 x right parenthesis end cell equals cell negative 1 half end cell row cell cos left parenthesis 2 x right parenthesis end cell equals cell cos left parenthesis 120 degree right parenthesis end cell row cell 2 x end cell equals cell 120 degree plus k times 360 degree end cell row x equals cell 60 degree plus 180 degree k end cell row blank blank blank end table$

atau

$table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x end cell equals cell negative 120 degree plus k times 360 degree end cell row x equals cell negative 60 degree plus 180 degree k end cell row blank blank blank end table$

Untuk $k equals 0$ , maka $x equals 60 degree space dan space x equals negative 60 degree left parenthesis T M right parenthesis$

Untuk $k equals 1$ , maka $x equals 240 degree left parenthesis T M right parenthesis space dan space x equals 120 degree$

Sehingga nilai x yang memenuhi adalah $x equals 60 degree space dan space x equals 120 degree$

Oleh karena itu, jawaban yang benar adalah D.

Roboguru

Diketahui g(x)=tan2(π−3x). Nilai dxd(g(4π))=....

Pembahasan Soal:

Diketahui $g left parenthesis x right parenthesis equals tan squared left parenthesis straight pi minus 3 straight x right parenthesis$ . Misal $tan space left parenthesis straight pi minus 3 straight x right parenthesis equals u rightwards arrow fraction numerator d u over denominator d x end fraction equals negative 3 s e c squared left parenthesis straight pi minus 3 straight x right parenthesis$ , sehingga

$table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis x right parenthesis end cell equals cell tan squared left parenthesis straight pi minus 3 straight x right parenthesis end cell row blank equals cell u squared end cell row cell g apostrophe left parenthesis x right parenthesis end cell equals cell 2 u times u apostrophe end cell row blank equals cell 2 tan left parenthesis straight pi minus 3 straight x right parenthesis times negative 3 s e c squared left parenthesis straight pi minus 3 straight x right parenthesis end cell row blank equals cell negative 3 left parenthesis 2 tan left parenthesis straight pi minus 3 straight x right parenthesis s e c squared left parenthesis straight pi minus 3 straight x right parenthesis right parenthesis end cell row cell straight d over dx open parentheses straight g open parentheses straight pi over 4 close parentheses close parentheses end cell equals cell straight g apostrophe open parentheses straight pi over 4 close parentheses end cell row blank equals cell negative 6 tan open parentheses straight pi minus 3 straight pi over 4 close parentheses sec squared open parentheses straight pi minus 3 straight pi over 4 close parentheses end cell row blank equals cell negative 6 space tan open parentheses straight pi over 4 close parentheses sec squared open parentheses straight pi over 4 close parentheses end cell row blank equals cell fraction numerator negative 6 left parenthesis 1 right parenthesis over denominator cos squared open parentheses begin display style straight pi over 4 end style close parentheses end fraction end cell row blank equals cell fraction numerator negative 6 over denominator open parentheses begin display style fraction numerator square root of 2 over denominator 2 end fraction end style close parentheses squared end fraction end cell row blank equals cell fraction numerator negative 24 over denominator 2 end fraction end cell row blank equals cell negative 12 end cell end table$

Oleh karena itu, jawaban yang benar adalah A.

Roboguru