Tentukan periode, nilai maksimum, nilai minimum, dan amplitudo fungsi berikut: e. y=3 cos (2x−30∘)

Pertanyaan

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

e. $y=3\;\cos\;\left(2x-30^\circ\right)$

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Pembahasan

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 3 space cos space open parentheses 2 x minus 30 degree close parentheses , dengan a equals 3 , k equals 2 , b equals negative 30 degree , dan c equals 0 .

Sehingga diperoleh:

$table attributes columnalign left center left end attributes row Periode equals cell fraction numerator 2 straight pi over denominator open vertical bar k close vertical bar end fraction end cell row Periode equals cell fraction numerator 2 times 180 degree over denominator open vertical bar 2 close vertical bar end fraction end cell row Periode equals cell fraction numerator 360 degree over denominator 2 end fraction end cell row Periode equals cell 180 degree end cell row space space space row cell Nilai space maksimum end cell equals cell open vertical bar a close vertical bar plus c end cell row cell Nilai space maksimum end cell equals cell open vertical bar 3 close vertical bar plus 0 end cell row cell Nilai space maksimum end cell equals 3 row space space space row cell Nilai space minimum end cell equals cell negative open vertical bar a close vertical bar plus c end cell row cell Nilai space minimum end cell equals cell negative open vertical bar 3 close vertical bar plus 0 end cell row cell Nilai space minimum end cell equals cell negative 3 end cell row space space space row Amplitudo equals cell 1 half open parentheses Nilai space maks minus Nilai space min close parentheses end cell row Amplitudo equals cell 1 half open parentheses 3 minus open parentheses negative 3 close parentheses close parentheses end cell row Amplitudo equals cell 1 half open parentheses 3 plus 3 close parentheses end cell row Amplitudo equals cell 1 half open parentheses 6 close parentheses end cell row Amplitudo equals 3 end table$