Pertanyaan

Tentukan himpunan penyelesaian tiap persamaan berikut untuk 0 ∘ ≤ x ≤ 36 0 ∘ . c. sin 2 x ⋅ sin ( 2 x + 6 0 ∘ ) = 2 1

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

c. $sin 2 x \cdot sin (2 x + 6 0^{\circ}) = \frac{1}{2}$

S. Yoga

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

Himpunan penyelesaian persamaan adalah .

Himpunan penyelesaian persamaan sin space 2 x times sin space left parenthesis 2 x plus 60 degree right parenthesis equals 1 half

adalah

HP equals left curly bracket 15 degree comma space 45 degree comma space 105 degree comma space 135 degree comma space 195 degree comma space 225 degree comma space 285 degree comma space 315 degree right curly bracket

Pembahasan

Ingat bahwa: Himpunan penyelesaian persamaan : Yang memenuhi adalah: Jadi, Himpunan penyelesaian persamaan adalah .

Ingat bahwa:

Himpunan penyelesaian persamaan sin space 2 x times sin space left parenthesis 2 x plus 60 degree right parenthesis equals 1 half :

$table attributes columnalign right center left columnspacing 0px end attributes row cell sin open parentheses 2 x close parentheses sin open parentheses 2 x plus 60 degree close parentheses end cell equals cell 1 half end cell row cell sin open parentheses 2 x close parentheses open parentheses 1 half sin open parentheses 2 x close parentheses plus fraction numerator square root of 3 over denominator 2 end fraction cos open parentheses 2 x close parentheses close parentheses end cell equals cell 1 half end cell row cell fraction numerator negative 1 plus sin squared open parentheses 2 x close parentheses plus square root of 3 sin open parentheses 2 x close parentheses cos open parentheses 2 x close parentheses over denominator 2 end fraction end cell equals 0 row cell negative 1 plus sin squared open parentheses 2 x close parentheses plus square root of 3 sin open parentheses 2 x close parentheses cos open parentheses 2 x close parentheses end cell equals 0 row cell negative cos squared open parentheses 2 x close parentheses plus cos open parentheses 2 x close parentheses sin open parentheses 2 x close parentheses square root of 3 end cell equals 0 row cell cos open parentheses 2 x close parentheses open parentheses negative cos open parentheses 2 x close parentheses plus square root of 3 sin open parentheses 2 x close parentheses close parentheses end cell equals 0 end table$

$cos open parentheses 2 x close parentheses equals 0 space atau thin space minus cos open parentheses 2 x close parentheses plus square root of 3 sin open parentheses 2 x close parentheses equals 0 cos open parentheses 2 x close parentheses equals 0 space atau thin space minus 1 plus square root of 3 tan open parentheses 2 x close parentheses equals 0 cos open parentheses 2 x close parentheses equals 0 space atau thin space square root of 3 tan open parentheses 2 x close parentheses equals 1 cos open parentheses 2 x close parentheses equals 0 space atau thin space tan open parentheses 2 x close parentheses equals fraction numerator square root of 3 over denominator 3 end fraction space cos open parentheses 2 x close parentheses equals 0 x equals 45 degree plus 180 degree thin space n comma thin space x equals 135 degree plus 180 degree n tan open parentheses 2 x close parentheses equals fraction numerator square root of 3 over denominator 3 end fraction thin space x equals 15 degree plus fraction numerator 180 degree n over denominator 2 end fraction$

Yang memenuhi 0 degree less or equal than x less or equal than 360 degree adalah:

$table attributes columnalign center left center end attributes row blank cell x equals 45 degree plus 180 degree n end cell blank row cell x equals 0 rightwards arrow end cell cell x equals 45 degree end cell blank row cell x equals 1 rightwards arrow end cell cell x equals 225 degree end cell blank row blank cell x equals 135 degree plus 180 degree n end cell blank row cell x equals 0 rightwards arrow end cell cell x equals 135 degree end cell blank row cell x equals 1 rightwards arrow end cell cell x equals 315 degree end cell blank row blank cell x equals 15 degree plus fraction numerator 180 degree n over denominator 2 end fraction end cell blank row cell x equals 0 rightwards arrow end cell cell x equals 15 degree end cell blank row cell x equals 1 rightwards arrow end cell cell x equals 105 degree end cell blank row cell x equals 2 rightwards arrow end cell cell x equals 195 degree end cell blank row cell x equals 3 rightwards arrow end cell cell x equals 285 degree end cell blank end table$

Jadi, Himpunan penyelesaian persamaan sin space 2 x times sin space left parenthesis 2 x plus 60 degree right parenthesis equals 1 half adalah HP equals left curly bracket 15 degree comma space 45 degree comma space 105 degree comma space 135 degree comma space 195 degree comma space 225 degree comma space 285 degree comma space 315 degree right curly bracket .