RoboguruRoboguru
SD

Himpunan penyelesaian dari sin (2x−31​π)=21​ untuk 0∘≤x≤2π adalah ....

Pertanyaan

Himpunan penyelesaian dari sin space left parenthesis 2 x minus 1 third straight pi right parenthesis equals 1 half untuk 0 degree less or equal than x less or equal than 2 straight pi adalah ....

  1. left curly bracket 1 fourth straight pi comma space 5 over 12 straight pi comma space 19 over 12 straight pi comma space 7 over 4 straight pi right curly bracket 

  2.  left curly bracket 1 fourth straight pi comma space 7 over 12 straight pi comma space 19 over 12 straight pi comma space 7 over 4 straight pi right curly bracket

  3.  left curly bracket 1 fourth straight pi comma space 7 over 12 straight pi comma space 3 over 4 straight pi comma space 19 over 12 straight pi right curly bracket

  4. left curly bracket 1 fourth straight pi comma space 5 over 12 straight pi comma space 5 over 4 straight pi comma space 17 over 12 straight pi right curly bracket

  5. left curly bracket 1 fourth straight pi comma space 7 over 12 straight pi comma space 5 over 4 straight pi comma space 19 over 12 straight pi right curly bracket  

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah A.

Ingat sin space x equals a diubah dahulu menjadi sin space x equals sin space alpha.

Jika sin space x equals sin space alpha, maka

  • x equals alpha plus k times 2 straight pi
  • x equals left parenthesis straight pi minus alpha right parenthesis plus k times 2 straight pi

Diketahui sin space left parenthesis 2 x minus 1 third straight pi right parenthesis equals 1 half untuk 0 degree 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 left parenthesis 2 x minus 1 third straight pi right parenthesis end cell equals cell 1 half end cell row blank equals cell sin space 30 degree end cell row cell sin space left parenthesis 2 x minus 1 third straight pi right parenthesis end cell equals cell sin space 1 over 6 straight pi end cell end table

  • table attributes columnalign right center left columnspacing 0px end attributes row cell bold 2 bold italic x bold minus bold 1 over bold 3 bold pi end cell bold equals cell bold 1 over bold 6 bold pi bold plus bold italic k bold times bold 2 bold pi end cell row cell 2 x end cell equals cell 1 half straight pi plus k times 2 straight pi end cell row x equals cell 1 fourth straight pi plus k times straight pi end cell row blank blank blank end table

            untuk k equals 0

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell 1 fourth straight pi plus 0 times straight pi end cell row blank equals cell 1 fourth straight pi plus 0 end cell row blank equals cell 1 fourth straight pi space left parenthesis memenuhi right parenthesis end cell row blank blank blank end table

            untuk k equals 1

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell 1 fourth straight pi plus 1 times straight pi end cell row blank equals cell fraction numerator straight pi plus 4 straight pi over denominator 4 end fraction end cell row blank equals cell 5 over 4 straight pi space left parenthesis memenuhi right parenthesis end cell row blank blank blank end table

            untuk k equals 2

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell 1 fourth straight pi plus 2 times straight pi end cell row blank equals cell fraction numerator straight pi plus 8 straight pi over denominator 4 end fraction end cell row blank equals cell 9 over 4 straight pi space left parenthesis tidak space memenuhi right parenthesis end cell row blank blank blank end table

  • table attributes columnalign right center left columnspacing 0px end attributes row cell bold 2 bold italic x bold minus bold 1 over bold 3 bold pi end cell bold equals cell bold left parenthesis bold pi bold minus bold 1 over 6 bold pi bold right parenthesis bold plus bold italic k bold times bold 2 bold pi end cell row cell 2 x end cell equals cell 7 over 6 straight pi plus k times 2 straight pi end cell row x equals cell 7 over 12 straight pi plus k times straight pi end cell end table

            untuk k equals 0

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell 7 over 12 straight pi plus 0 times straight pi end cell row blank equals cell 7 over 12 straight pi plus 0 end cell row blank equals cell 7 over 12 straight pi space left parenthesis memenuhi right parenthesis end cell row blank blank blank end table

            untuk k equals 1

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell 7 over 12 straight pi plus 1 times straight pi end cell row blank equals cell fraction numerator 7 straight pi plus 12 straight pi over denominator 12 end fraction end cell row blank equals cell 19 over 12 straight pi space left parenthesis memenuhi right parenthesis end cell row blank blank blank end table

            untuk k equals 2

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell 7 over 12 straight pi plus 2 times straight pi end cell row blank equals cell fraction numerator 7 straight pi plus 24 straight pi over denominator 12 end fraction end cell row blank equals cell 31 over 12 straight pi space left parenthesis tidak space memenuhi right parenthesis end cell row blank blank blank end table

Jadi, himpunan penyelesaiannya adalah left curly bracket 1 fourth straight pi comma space 5 over 12 straight pi comma space 19 over 12 straight pi comma space 7 over 4 straight pi right curly bracket.

Oleh karena itu, jawaban yang benar adalah A.

62

0.0 (0 rating)

Pertanyaan serupa

Selesaikanlah persamaan berikut untuk 0∘<x<360∘ sin (3x−45)∘+sin (x−15)∘=0

69

0.0

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

Produk Lainnya

Hubungi Kami

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia