Iklan

Iklan

Pertanyaan

Tentukan nilai x yang memenuhi untuk 0 ∘ ≤ x ≤ 36 0 ∘ . 2. cos 3 x = 2 1 ​

Tentukan nilai  yang memenuhi untuk .

2.  

Iklan

W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

nilai yang memenuhi adalah .

nilai straight x yang memenuhi adalah open curly brackets 20 degree comma space 100 degree comma space 140 degree comma space 220 degree comma space 260 degree comma space space 340 degree close curly brackets.

Iklan

Pembahasan

Ingat kembali: Maka: Sehingga: - Persamaan (1) - Persamaan (2) Jadi, nilai yang memenuhi adalah .

Ingat kembali:

cos space straight x equals cos space straight alpha rightwards arrow open curly brackets table attributes columnalign left end attributes row cell straight x equals straight alpha plus straight k times 360 degree end cell row cell straight x equals negative straight alpha plus straight k times 360 degree end cell end table close 

Maka:

cos space 3 straight x equals 1 half cos space 3 straight x equals cos space 60 degree 

Sehingga:

- Persamaan (1)

3 straight x equals 60 degree plus straight k times 360 degree space space space straight x equals 20 degree plus straight k times 120 degree 

straight k equals 0 rightwards arrow straight x equals 20 degree plus straight k times 120 degree equals 20 degree plus 0 times 120 degree equals 20 degree space open parentheses Memenuhi close parentheses straight k equals 1 rightwards arrow straight x equals 20 degree plus straight k times 120 degree equals 20 degree plus 1 times 120 degree equals 140 degree space open parentheses Memenuhi close parentheses straight k equals 2 rightwards arrow straight x equals 20 degree plus straight k times 120 degree equals 20 degree plus 2 times 120 degree equals 260 degree space open parentheses Memenuhi close parentheses straight k equals 3 rightwards arrow straight x equals 20 degree plus straight k times 120 degree equals 20 degree plus 3 times 120 degree equals 380 degree space open parentheses Tidak space Memenuhi close parentheses 

- Persamaan (2)

3 straight x equals negative 60 degree plus straight k times 360 degree space space space straight x equals negative 20 degree plus straight k times 120 degree 

straight k equals 0 rightwards arrow straight x equals negative 20 degree plus straight k times 120 degree equals negative 20 degree plus 0 times 120 degree equals negative 20 degree space open parentheses Tidak space Memenuhi close parentheses straight k equals 1 rightwards arrow straight x equals negative 20 degree plus straight k times 120 degree equals negative 20 degree plus 1 times 120 degree equals 100 degree space open parentheses Memenuhi close parentheses straight k equals 2 rightwards arrow straight x equals negative 20 degree plus straight k times 120 degree equals negative 20 degree plus 2 times 120 degree equals 220 degree space open parentheses Memenuhi close parentheses straight k equals 3 rightwards arrow straight x equals negative 20 degree plus straight k times 120 degree equals negative 20 degree plus 3 times 120 degree equals 340 degree space open parentheses Memenuhi close parentheses straight k equals 4 rightwards arrow straight x equals negative 20 degree plus straight k times 120 degree equals negative 20 degree plus 4 times 120 degree equals 460 degree space open parentheses Tidak space Memenuhi close parentheses 

Jadi, nilai straight x yang memenuhi adalah open curly brackets 20 degree comma space 100 degree comma space 140 degree comma space 220 degree comma space 260 degree comma space space 340 degree close curly brackets.

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

86

Iklan

Iklan

Pertanyaan serupa

Untuk 0 ∘ ≤ x ≤ 36 0 ∘ , tentukan himpunan penyelesaiandari persamaan trigonometri di bawah ini : 3 sin x + 5 cos x + 5 = 0

1

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

[email protected]

Contact 02140008000

02140008000

Ikuti Kami

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