Iklan

Iklan

Pertanyaan

Himpunan penyelesaian dari persamaan 3 ​ sin x − 3 cos x = 3 ​ untuk 0 ≤ x ≤ 2 π adalah...

Himpunan penyelesaian dari persamaan  untuk  adalah...

  1. open curly brackets 1 half straight pi comma space 7 over 6 straight pi close curly brackets

  2. open curly brackets 1 half straight pi comma space 5 over 6 straight pi close curly brackets

  3. open curly brackets straight pi comma space 7 over 6 straight pi close curly brackets

  4. open curly brackets straight pi comma space 5 over 6 straight pi close curly brackets

  5. open curly brackets 5 over 6 straight pi comma space 7 over 6 straight pi close curly brackets

Iklan

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

jawaban yang benar adalah A.

Iklan

Pembahasan

Pembahasan
lock

Dengan mengggunakan rumus trigonometri, misalkan, Sehingga, Kemudian, Jadi, . Oleh karena itu, jawaban yang benar adalah A.

Dengan mengggunakan rumus trigonometri, misalkan,

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 3 sin space x minus 3 cos space x end cell equals cell k cos left parenthesis x plus alpha right parenthesis degree end cell row blank equals cell k cos space x degree times cos space alpha degree minus k sin space x degree times sin space alpha degree end cell end table

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell k cos space alpha degree end cell equals cell negative 3 end cell row cell k sin space alpha degree end cell equals cell negative square root of 3 end cell row k equals cell square root of open parentheses negative 3 close parentheses squared plus open parentheses negative square root of 3 close parentheses squared end root end cell row blank equals cell square root of 9 plus 3 end root end cell row blank equals cell square root of 12 end cell row blank equals cell 2 square root of 3 end cell row cell tan space alpha degree end cell equals cell fraction numerator negative square root of 3 over denominator negative 3 end fraction space left parenthesis kuadran space III right parenthesis end cell row blank equals cell 1 third square root of 3 end cell row cell alpha degree end cell equals cell 210 degree end cell end table

Kemudian,

table attributes columnalign right center left columnspacing 0px end attributes row cell k cos space left parenthesis x plus alpha right parenthesis degree end cell equals cell 2 square root of 3 cos space left parenthesis x plus 210 right parenthesis degree equals square root of 3 end cell row blank left right double arrow cell cos space left parenthesis x plus 210 right parenthesis degree equals 1 half end cell row cell cos space left parenthesis x plus 210 right parenthesis degree end cell equals cell 1 half end cell row cell cos space left parenthesis x plus 210 right parenthesis degree end cell equals cell cos space 60 degree end cell row cell space x plus 210 degree end cell equals cell plus-or-minus 60 degree plus n times 360 degree end cell row x equals cell negative 150 degree plus n times 360 degree end cell row cell untuk space n end cell equals cell 0 comma space 1 end cell row x equals cell negative 150 degree plus 0 times 360 degree end cell row blank equals cell negative 150 degree end cell row x equals cell negative 150 degree plus 1 times 360 degree end cell row blank equals cell 210 degree end cell row cell atau space x end cell equals cell negative 270 degree plus n times 360 degree end cell row n equals cell 0 comma space 1 end cell row x equals cell negative 270 degree plus 0 times 360 degree end cell row blank equals cell negative 270 degree end cell row x equals cell negative 270 degree plus 1 times 360 degree end cell row blank equals cell 90 degree end cell end table

Jadi, 

table attributes columnalign right center left columnspacing 0px end attributes row HP equals cell open curly brackets 90 degree comma space 210 degree close curly brackets end cell row blank equals cell open curly brackets 1 half straight pi comma space 7 over 6 straight pi close curly brackets end cell end table.


Oleh karena itu, jawaban yang benar adalah A.

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

191

Iklan

Iklan

Pertanyaan serupa

Selesaikanlah persamaan berikut untuk 0 ∘ < x < 36 0 ∘ 3 sin 2 x + 4 sin x ⋅ cos x − cos 2 x = 2

60

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

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