Pertanyaan

Tentukan penyelesaian dari setiap persamaan trigonometri berikut. b. sin 3 1 x = sin 9 π , 0 ≤ x ≤ 2 π

Tentukan penyelesaian dari setiap persamaan trigonometri berikut.

b. $sin \frac{1}{3} x = sin \frac{π}{9}, 0 \leq x \leq 2 π$

W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

solusi dan himpunan penyelesaian persamaan trigonometri adalah .

solusi dan himpunan penyelesaian persamaan trigonometri sin space 1 third x equals sin space straight pi over 9 comma space 0 less or equal than x less or equal than 2 straight pi

sin space 1 third x equals sin space straight pi over 9 comma space 0 less or equal than x less or equal than 2 straight pi

adalah

HP equals open curly brackets straight pi over 3 close curly brackets

Pembahasan

Ingat kembali aturan penyelesaian persamaan trigonometri berikut: Diketahui persamaan trigonometri . Maka: Sehingga: - Persamaan - Persamaan Jadi, solusi dan himpunan penyelesaian persamaan trigonometri adalah .

Ingat kembali aturan penyelesaian persamaan trigonometri berikut:

sin space x equals sin space alpha rightwards double arrow open curly brackets table attributes columnalign left end attributes row cell x equals alpha plus 2 straight pi k end cell row cell x equals open parentheses straight pi minus straight alpha close parentheses plus 2 straight pi k end cell end table close

Diketahui persamaan trigonometri sin space 1 third x equals sin space straight pi over 9 comma space 0 less or equal than x less or equal than 2 straight pi . Maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space x end cell equals cell sin space alpha end cell row cell sin space 1 third x end cell equals cell sin space straight pi over 9 end cell end table

Sehingga:

- Persamaan

$table attributes columnalign right center left columnspacing 0px end attributes row x equals cell alpha plus 2 straight pi k end cell row cell 1 third x end cell equals cell straight pi over 9 plus 2 straight pi k end cell row x equals cell fraction numerator straight pi over 9 plus 2 straight pi k over denominator begin display style 1 third end style end fraction end cell row x equals cell open square brackets straight pi over 9 plus 2 straight pi k close square brackets cross times 3 over 1 end cell row x equals cell straight pi over 3 plus 6 straight pi k end cell end table$

- Persamaan

$table attributes columnalign right center left columnspacing 0px end attributes row x equals cell open parentheses straight pi minus straight alpha close parentheses plus 2 straight pi k end cell row cell 1 third x end cell equals cell open parentheses straight pi minus straight pi over 9 close parentheses plus 2 straight pi k end cell row cell 1 third x end cell equals cell 8 over 9 straight pi plus 2 straight pi k end cell row x equals cell fraction numerator 8 over 9 straight pi plus 2 straight pi k over denominator begin display style 1 third end style end fraction end cell row x equals cell open parentheses 8 over 9 straight pi plus 2 straight pi k close parentheses cross times 3 over 1 end cell row x equals cell 8 over 3 straight pi plus 6 straight pi k end cell end table$

Jadi, solusi dan himpunan penyelesaian persamaan trigonometri sin space 1 third x equals sin space straight pi over 9 comma space 0 less or equal than x less or equal than 2 straight pi adalah HP equals open curly brackets straight pi over 3 close curly brackets .