Pertanyaan

Tentukan periode, nilai maksimum, nilai minimum, dan amplitudo fungsi berikut: f. y = 2 cos ( 3 x + 6 0 ∘ ) − 1

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

f. $y = 2 cos (3 x + 6 0^{\circ}) - 1$

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Pembahasan

Bentuk umum fungsi cosinus adalah . Dengan: Fungsi , dengan , , , dan . Sehingga diperoleh:

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 2 space cos space open parentheses 3 x plus 60 degree close parentheses minus 1 , dengan a equals 2 , k equals 3 , b equals 60 degree , dan c equals negative 1 .

Sehingga diperoleh:

$table attributes columnalign left center left end attributes row Periode equals cell fraction numerator 2 straight pi over denominator open vertical bar k close vertical bar end fraction end cell row Periode equals cell fraction numerator 2 times 180 degree over denominator open vertical bar 3 close vertical bar end fraction end cell row Periode equals cell fraction numerator 360 degree over denominator 3 end fraction end cell row Periode equals cell 120 degree end cell row space space space row cell Nilai space maksimum end cell equals cell open vertical bar a close vertical bar plus c end cell row cell Nilai space maksimum end cell equals cell open vertical bar 2 close vertical bar plus open parentheses negative 1 close parentheses end cell row cell Nilai space maksimum end cell equals cell 2 minus 1 end cell row cell Nilai space maksimum end cell equals 1 row space space space row cell Nilai space minimum end cell equals cell negative open vertical bar a close vertical bar plus c end cell row cell Nilai space minimum end cell equals cell negative open vertical bar 2 close vertical bar plus open parentheses negative 1 close parentheses end cell row cell Nilai space minimum end cell equals cell negative 2 minus 1 end cell row cell Nilai space minimu end cell equals cell negative 3 end cell row space space space row Amplitudo equals cell 1 half open parentheses Nilai space maks minus Nilai space min close parentheses end cell row Amplitudo equals cell 1 half open parentheses 1 minus open parentheses negative 3 close parentheses close parentheses end cell row Amplitudo equals cell 1 half open parentheses 1 plus 3 close parentheses end cell row Amplitudo equals cell 1 half open parentheses 4 close parentheses end cell row Amplitudo equals 2 end table$