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Tentukan periode, nilai maksimum, nilai minimum, dan amplitudo fungsi berikut: b.

Pertanyaan

Tentukan periode, nilai maksimum, nilai minimum, dan amplitudo fungsi berikut:

b. y equals cos space open parentheses x plus 30 degree close parentheses

Pembahasan Soal:

Bentuk umum fungsi cosinus adalah y equals a space cos space open parentheses k x plus-or-minus b close parentheses plus c.

Dengan:

table attributes columnalign left center left end attributes row Periode equals cell fraction numerator 2 straight pi over denominator open vertical bar k close vertical bar end fraction end cell row Amplitudo equals cell 1 half open parentheses Nilai space maks minus Nilai space min close parentheses end cell row cell Nilai space maksimum end cell equals cell open vertical bar a close vertical bar plus c end cell row cell Nilai space minimum end cell equals cell negative open vertical bar a close vertical bar plus c end cell end table

Fungsi y equals cos space open parentheses x plus 30 degree close parentheses, dengan a equals 1k equals 1, b equals 30 degree, dan c equals 0.

Sehingga diperoleh:

table attributes columnalign left center left end attributes row Periode equals cell fraction numerator 2 straight pi over denominator open vertical bar k close vertical bar end fraction end cell row Periode equals cell fraction numerator 2 times 180 degree over denominator open vertical bar 1 close vertical bar end fraction end cell row Periode equals cell 360 degree end cell row space space space row cell Nilai space maksimum end cell equals cell open vertical bar a close vertical bar plus c end cell row cell Nilai space maksimum end cell equals cell open vertical bar 1 close vertical bar plus 0 end cell row cell Nilai space maksimum end cell equals 1 row space space space row cell Nilai space minimum end cell equals cell negative open vertical bar a close vertical bar plus c end cell row cell Nilai space minimum end cell equals cell negative open vertical bar 1 close vertical bar plus 0 end cell row cell Nilai space minimum end cell equals cell negative 1 end cell row space space space row Amplitudo equals cell 1 half open parentheses Nilai space maks minus Nilai space min close parentheses end cell row Amplitudo equals cell 1 half open parentheses 1 minus open parentheses negative 1 close parentheses close parentheses end cell row Amplitudo equals cell 1 half open parentheses 1 plus 1 close parentheses end cell row Amplitudo equals cell 1 half open parentheses 2 close parentheses end cell row Amplitudo equals 1 end table

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 10 Juni 2021

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