Roboguru

Tentukan penyelesaian dari setiap persamaan trigonometri berikut. a. tan21​x=tan6π​,0≤x≤2π

Pertanyaan

Tentukan penyelesaian dari setiap persamaan trigonometri berikut.

a. tan space 1 half x equals tan space straight pi over 6 comma space 0 less or equal than x less or equal than 2 straight pi 

Pembahasan:

Ingat kembali aturan penyelesaian persamaan trigonometri berikut:

tan space x equals tan space alpha rightwards double arrow x equals alpha plus πk 

Diketahui persamaan trigonometri tan space 1 half x equals tan space straight pi over 6 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 tan space x end cell equals cell tan space alpha end cell row cell tan space 1 half x end cell equals cell tan space straight pi over 6 end cell end table 

Sehingga:

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

begin mathsize 12px style k equals negative 1 rightwards arrow table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight pi over 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight pi end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank k end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight pi over 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight pi end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses negative 1 close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 5 over 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight pi end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses TM close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank k end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 0 end table table attributes columnalign right center left columnspacing 0px end attributes row blank rightwards arrow blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight x end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight pi over 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight pi end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight k end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight pi over 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight pi end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 0 close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight pi over 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses straight M close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank k end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 1 end table table attributes columnalign right center left columnspacing 0px end attributes row blank rightwards arrow blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight x end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight pi over 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight pi end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight k end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight pi over 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight pi end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 1 close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 7 over 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight pi end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses TM close parentheses end cell end table end style 

Jadi, penyelesaian persamaan trigonometri tan space 1 half x equals tan space straight pi over 6 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.

Jawaban terverifikasi

Dijawab oleh:

W. Lestari

Mahasiswa/Alumni Universitas Sriwijaya

Terakhir diupdate 07 Oktober 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

Pertanyaan serupa

Jika tant=tan70∘ untuk 90∘≤t≤270∘, nilai t adalah....

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

RUANGGURU HQ

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

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved