Pertanyaan

Tentukan himpunan penyelesaian tiap persamaan berikut untuk 0 ∘ ≤ x ≤ 36 0 ∘ . b. cos ( 2 x + 3 0 ∘ ) + cos ( 4 x − 6 0 ∘ ) = 0

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

b. $cos (2 x + 3 0^{\circ}) + cos (4 x - 6 0^{\circ}) = 0$

S. Yoga

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

himpunan penyelesaiannya adalah .

himpunan penyelesaiannya adalah HP equals open curly brackets 35 degree comma space 95 degree comma space 155 degree comma space 215 degree comma space 275 degree comma space 335 degree close curly brackets

HP equals open curly brackets 35 degree comma space 95 degree comma space 155 degree comma space 215 degree comma space 275 degree comma space 335 degree close curly brackets

Pembahasan

Ingat bahwa: Mencari himpunan penyelesaian: Sehingga didapat penyelesaiannya adalah . Yang memenuhi adalah: Didapat: Jadi,himpunan penyelesaiannya adalah .

Ingat bahwa:

Mencari himpunan penyelesaian:

$table attributes columnalign right center left columnspacing 0px end attributes row cell cos space left parenthesis 2 x plus 30 degree right parenthesis plus cos space left parenthesis 4 x minus 60 degree right parenthesis end cell equals 0 row cell 2 cos space open parentheses fraction numerator 6 x minus 30 degree over denominator 2 end fraction close parentheses cos space open parentheses fraction numerator negative 2 x plus 90 degree over denominator 2 end fraction close parentheses end cell equals 0 row cell 2 cos space open parentheses 3 x minus 15 degree close parentheses cos space open parentheses negative x plus 45 degree close parentheses end cell equals 0 row cell cos space open parentheses 3 x minus 15 degree close parentheses cos space open parentheses negative x plus 45 degree close parentheses end cell equals 0 end table$

$table attributes columnalign right center left columnspacing 0px end attributes row blank rightwards arrow cell cos space open parentheses 3 x minus 15 degree close parentheses equals 0 end cell row blank blank blank row blank rightwards arrow cell 3 x minus 15 degree equals 90 degree plus 360 degree n comma thin space end cell row x equals cell fraction numerator 360 degree n over denominator 3 end fraction plus 35 degree end cell row blank blank atau row cell 3 x minus 15 degree end cell equals cell 270 degree plus 360 degree n end cell row x equals cell fraction numerator 360 degree n over denominator 3 end fraction plus 95 degree end cell end table$

Sehingga didapat penyelesaiannya adalah $HP equals open curly brackets table attributes columnalign right center left columnspacing 0px end attributes row x equals cell negative 360 degree n minus 45 degree comma space atau end cell row x equals cell negative 360 degree n minus 225 degree comma space atau end cell row x equals cell fraction numerator 360 degree thin space n over denominator 3 end fraction plus 35 degree comma space atau end cell row x equals cell fraction numerator 360 degree n over denominator 3 end fraction plus 95 degree end cell end table close curly brackets$ .

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

$table attributes columnalign center left center end attributes row blank cell x equals negative 360 degree n minus 45 degree end cell blank row cell x equals 0 rightwards arrow end cell cell x equals negative 45 degree end cell memenuhi row blank cell x equals negative 360 degree n minus 225 degree end cell blank row cell x equals 0 rightwards arrow end cell cell x equals negative 225 degree end cell memenuhi row blank cell x equals fraction numerator 360 degree n over denominator 3 end fraction plus 35 degree end cell blank row cell x equals 0 rightwards arrow end cell cell x equals 35 degree end cell memenuhi row cell x equals 1 rightwards arrow end cell cell x equals 155 degree end cell memenuhi row cell x equals 2 rightwards arrow end cell cell x equals 275 degree end cell memenuhi row blank cell x equals fraction numerator 360 degree n over denominator 3 end fraction plus 95 degree end cell blank row cell x equals 0 rightwards arrow end cell cell x equals 95 degree end cell memenuhi row cell x equals 1 rightwards arrow end cell cell x equals 215 degree end cell memenuhi row cell x equals 2 rightwards arrow end cell cell x equals 335 degree end cell memenuhi end table$

Didapat:

HP equals open curly brackets 35 degree comma space 95 degree comma space 155 degree comma space 215 degree comma space 275 degree comma space 335 degree close curly brackets

Jadi, himpunan penyelesaiannya adalah HP equals open curly brackets 35 degree comma space 95 degree comma space 155 degree comma space 215 degree comma space 275 degree comma space 335 degree close curly brackets .