Iklan

Iklan

Pertanyaan

Tentukan himpunan penyelesaian dari persamaan berikut untuk − 36 0 ∘ ≤ x ≤ 36 0 ∘ cos 4 x ∘ + cos 2 x ∘ = 0

Tentukan himpunan penyelesaian dari persamaan berikut untuk 

Iklan

Z. Apriani

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Iklan

Pembahasan

Dengan menggunakan rumus trigonometri, misalkan Sehingga, atau Dengan demikian,

Dengan menggunakan rumus trigonometri, misalkan cos space 2 x degree equals y

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space 4 x degree plus cos space 2 x degree end cell equals 0 row cell open parentheses 2 cos squared space 2 x degree minus 1 close parentheses plus cos space 2 x degree end cell equals 0 row cell 2 open parentheses cos space 2 x degree close parentheses squared plus cos space 2 x degree minus 1 end cell equals 0 row cell 2 y squared plus y minus 1 end cell equals 0 row cell left parenthesis 2 y minus 1 right parenthesis left parenthesis y plus 1 right parenthesis end cell equals 0 row cell 2 y end cell equals 1 row y equals cell 1 half end cell row cell cos space 2 x degree end cell equals cell 1 half space atau end cell row y equals cell negative 1 end cell row cell cos space 2 x degree end cell equals cell negative 1 end cell end table

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space 2 x degree end cell equals cell 1 half end cell row cell cos space 2 x degree end cell equals cell cos space 60 degree end cell row cell 2 x end cell equals cell 60 degree plus n times 360 degree space end cell row x equals cell 30 degree plus 0 times 180 degree end cell row blank equals cell 30 degree end cell row x equals cell 30 degree plus 1 times 180 degree end cell row blank equals cell 210 degree end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space 2 x degree end cell equals cell 1 half end cell row cell cos space 2 x degree end cell equals cell cos space 60 degree end cell row cell 2 x end cell equals cell negative 60 degree plus n times 360 degree space end cell row x equals cell negative 30 degree plus 0 times 180 degree end cell row blank equals cell negative 30 degree end cell row x equals cell negative 30 degree plus 1 times 180 degree end cell row blank equals cell 150 degree end cell row x equals cell negative 30 degree plus 2 times 180 degree end cell row blank equals cell 330 degree end cell end table

atau

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space 2 x degree end cell equals cell negative 1 end cell row cell cos space 2 x degree end cell equals cell cos space 180 degree end cell row cell 2 x end cell equals cell 180 degree plus n times space 360 degree end cell row x equals cell 90 degree plus n times space 180 degree end cell row x equals cell 90 degree plus 0 times space 180 degree end cell row blank equals cell 90 degree end cell row x equals cell 90 degree plus 1 times space 180 degree end cell row blank equals cell 270 degree end cell row blank blank atau row cell 2 x end cell equals cell negative 180 degree plus n times 360 degree end cell row x equals cell negative 90 degree plus 0 times space 180 degree end cell row blank equals cell negative 90 degree end cell row x equals cell negative 90 degree plus 1 times space 180 degree end cell row blank equals cell 90 degree end cell row x equals cell negative 90 degree plus 2 times space 180 degree end cell row blank equals cell 270 degree end cell end table

Dengan demikian,

HP equals open curly brackets negative 30 degree comma space minus 90 degree comma space 90 degree comma space 150 degree comma space 210 degree comma space 270 degree comma space 330 degree close curly brackets

Perdalam pemahamanmu bersama Master Teacher
di sesi Live Teaching, GRATIS!

24

Iklan

Iklan

Pertanyaan serupa

Tentukan himpunan penyelesaian dari persamaan-persamaan trigonometri berikut! b. cos 4 x = cos 10 0 ∘ , 0 ∘ ≤ x ≤ 36 0 ∘

1

5.0

Jawaban terverifikasi

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Hubungi Kami

Ruangguru WhatsApp

+62 815-7441-0000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2024 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia