Pertanyaan

Jika nilai maksimum dan nilai minimum fungsi pada 0 ∘ ≤ x ≤ 36 0 ∘ masing-masing adalah a dan b , maka a + b = …

Jika nilai maksimum dan nilai minimum fungsi pada $0^{\circ} \leq x \leq 36 0^{\circ}$ masing-masing adalah $a$ dan $b$ , maka $a + b = \dots$

Ikuti Tryout SNBT & Menangkan E-Wallet 100rb

Habis dalam

Klaim

Y. Endah

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Pembahasan

Nilai maksimum dan minimum dapat diperoleh saat , maka :

$begin mathsize 14px style f left parenthesis x right parenthesis equals cos space x minus sin space x plus 3 minus sin space x minus cos space x equals 0 minus sin space x equals cos space x fraction numerator sin space x over denominator cos space x end fraction equals negative 1 tan space x equals negative 1 text Kuadran II end text space colon space x equals 135 degree text Kuadran IV end text space colon space x equals 315 degree f open parentheses 0 degree close parentheses equals cos space 0 degree minus sin space 0 degree plus 3 equals 1 minus 0 plus 3 equals 4 f open parentheses 135 degree close parentheses equals cos space 135 degree minus sin space 135 degree plus 3 space space space space space space space space space space space space equals negative 1 half square root of 2 minus 1 half square root of 2 plus 3 space space space space space space space space space space space space equals 3 minus square root of 2 f open parentheses 315 degree close parentheses equals cos space 315 degree minus sin space 315 degree plus 3 space space space space space space space space space space space space equals 1 half square root of 2 plus 1 half square root of 2 plus 3 space space space space space space space space space space space space equals 3 plus square root of 2 f open parentheses 360 degree close parentheses equals cos space 360 degree minus sin space 360 degree plus 3 space space space space space space space space space space space space equals 1 minus 0 plus 3 space space space space space space space space space space space space equals 4 text Nilai maksimum end text equals a equals 3 plus square root of 2 text Nilai minimum end text equals b equals 3 minus square root of 2 text Jadi, nilai end text space a plus b equals 3 plus square root of 2 plus 3 minus square root of 2 equals 6 end style$