Pertanyaan

Tentukan himpunan penyelesaian tiap persamaan berikut untuk 0 ∘ ≤ x ≤ 36 0 ∘ . e. 2 cos ( 2 x + 3 0 ∘ ) cos ( 2 x − 6 0 ∘ ) = 2 1 3

Tentukan himpunan penyelesaian tiap persamaan berikut untuk $0^{\circ} \leq x \leq 36 0^{\circ}$ .

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

S. Yoga

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

himpunan penyelesaiannya adalah .

himpunan penyelesaiannya adalah HP equals left curly bracket 0 degree comma space 15 degree comma space 90 degree comma space 105 degree comma space 180 degree comma space 195 degree comma space 270 degree comma space 285 degree comma space 360 degree right curly bracket

HP equals left curly bracket 0 degree comma space 15 degree comma space 90 degree comma space 105 degree comma space 180 degree comma space 195 degree comma space 270 degree comma space 285 degree comma space 360 degree right curly bracket

Pembahasan

Ingat bahwa: Mencari himpunan penyelesaian: Dari penyelesaian tersebut, yang memenuhi adalah: Jadi, himpunan penyelesaiannya adalah .

Ingat bahwa:

Mencari himpunan penyelesaian:

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 cos open parentheses 2 x plus 30 to the power of ring operator thin space end exponent close parentheses cos open parentheses 2 x minus 60 to the power of ring operator thin space end exponent close parentheses end cell equals cell 1 half square root of 3 end cell row cell fraction numerator square root of 3 over denominator 2 end fraction cos squared open parentheses 2 x close parentheses plus sin open parentheses 2 x close parentheses cos open parentheses 2 x close parentheses minus fraction numerator square root of 3 over denominator 2 end fraction sin squared open parentheses 2 x close parentheses end cell equals cell fraction numerator square root of 3 over denominator 2 end fraction end cell row cell fraction numerator square root of 3 over denominator 2 end fraction cos squared open parentheses 2 x close parentheses plus sin open parentheses 2 x close parentheses cos open parentheses 2 x close parentheses minus fraction numerator square root of 3 over denominator 2 end fraction sin squared open parentheses 2 x close parentheses minus fraction numerator square root of 3 over denominator 2 end fraction end cell equals 0 row cell fraction numerator square root of 3 cos squared open parentheses 2 x close parentheses minus square root of 3 sin squared open parentheses 2 x close parentheses minus square root of 3 plus 2 sin open parentheses 2 x close parentheses cos open parentheses 2 x close parentheses over denominator 2 end fraction end cell equals 0 row cell fraction numerator square root of 3 cos squared open parentheses 2 x close parentheses minus square root of 3 sin squared open parentheses 2 x close parentheses minus square root of 3 plus 2 sin open parentheses 2 x close parentheses cos open parentheses 2 x close parentheses over denominator 2 end fraction end cell equals 0 row cell 2 cos open parentheses 2 x close parentheses sin open parentheses 2 x close parentheses minus 2 sin squared open parentheses 2 x close parentheses square root of 3 end cell equals 0 row cell 2 sin open parentheses 2 x close parentheses open parentheses cos open parentheses 2 x close parentheses minus square root of 3 sin open parentheses 2 x close parentheses close parentheses end cell equals 0 end table end style$

$sin open parentheses 2 x close parentheses equals 0 space atau space cos open parentheses 2 x close parentheses minus square root of 3 sin open parentheses 2 x close parentheses equals 0 x equals 180 degree n comma thin space x equals 90 degree plus 180 degree n comma thin space x equals 15 degree plus fraction numerator 180 degree n over denominator 2 end fraction$

Dari penyelesaian tersebut, yang memenuhi 0 degree less or equal than x less or equal than 360 degree adalah:

$table attributes columnalign center left center end attributes row blank cell x equals 180 degree n end cell blank row cell x equals 0 rightwards arrow end cell cell x equals 0 degree end cell blank row cell x equals 1 rightwards arrow end cell cell x equals 180 degree end cell blank row cell x equals 2 rightwards arrow end cell cell x equals 360 degree end cell blank row blank cell x equals 90 degree plus 180 degree n end cell blank row cell x equals 0 rightwards arrow end cell cell x equals 90 degree end cell blank row cell x equals 1 rightwards arrow end cell cell x equals 270 degree end cell blank row blank cell x equals 15 degree plus fraction numerator 180 degree n over denominator 2 end fraction end cell blank row cell x equals 0 rightwards arrow end cell cell x equals 15 degree end cell blank row cell x equals 1 rightwards arrow end cell cell x equals 105 degree end cell blank row cell x equals 2 rightwards arrow end cell cell x equals 195 degree end cell blank row cell x equals 3 rightwards arrow end cell cell x equals 285 degree end cell blank end table$

Jadi, himpunan penyelesaiannya adalah HP equals left curly bracket 0 degree comma space 15 degree comma space 90 degree comma space 105 degree comma space 180 degree comma space 195 degree comma space 270 degree comma space 285 degree comma space 360 degree right curly bracket .