Roboguru

8. Selesaikan setiap persamaan berikut untuk . d.

Pertanyaan

8. Selesaikan setiap persamaan berikut untuk 0 degree less or equal than x less or equal than 360 degree.

d. sin space open parentheses 2 theta plus 30 degree close parentheses equals 0 comma 134 

Pembahasan Soal:

Diasumsikan x equals theta.

Terlebih dahulu kita ubah fungsi trigonometri tersebut sebagai berikut:

sin space open parentheses 2 theta plus 30 degree close parentheses equals 0 comma 134 sin space open parentheses 2 theta plus 30 degree close parentheses equals sin space open parentheses 7 comma 7 degree close parentheses 

Berdasarkan rumus dasar trigonometri untuk sinus yaitu:

sin space x equals sin space A left right double arrow x equals A plus n times 360 space atau space x equals open parentheses 180 minus A close parentheses plus n times 360 

Maka dapat dituliskan:

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 theta plus 30 degree end cell equals cell 7 comma 7 degree plus n times 360 degree end cell row cell 2 theta end cell equals cell 7 comma 7 degree minus 30 degree plus n times 360 degree end cell row cell 2 theta end cell equals cell negative 22 comma 3 degree plus n times 360 degree end cell row theta equals cell fraction numerator negative 22 comma 3 degree plus n times 360 degree over denominator 2 end fraction end cell row theta equals cell negative 11 comma 15 degree plus n times 180 degree end cell end table 

 

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 theta plus 30 degree end cell equals cell open parentheses 180 minus 7 comma 7 close parentheses degree plus n times 360 degree end cell row cell 2 theta plus 30 degree end cell equals cell 172 comma 3 degree plus n times 360 degree end cell row cell 2 theta end cell equals cell 172 comma 3 degree minus 30 degree plus n times 360 degree end cell row cell 2 theta end cell equals cell 142 comma 3 degree plus n times 360 degree end cell row theta equals cell fraction numerator 142 comma 3 degree plus n times 360 degree over denominator 2 end fraction end cell row theta equals cell 71 comma 15 degree plus n times 180 degree end cell end table 

Sehingga diperoleh:

table row cell n equals 0 end cell rightwards double arrow cell theta subscript 1 equals negative 11.15 plus 0 equals negative 11 comma 15 space open parentheses TM close parentheses end cell row blank blank cell theta subscript 2 equals 71.15 plus 0 equals 71 comma 15 end cell row cell n equals 1 end cell rightwards double arrow cell theta subscript 3 equals negative 11.15 plus 180 equals 168 comma 85 end cell row blank blank cell theta subscript 4 equals 71.15 plus 180 equals 251 comma 15 end cell row cell n equals 2 end cell rightwards double arrow cell theta subscript 3 equals negative 11.15 plus 360 equals 348 comma 85 end cell row blank blank cell theta subscript 5 equals 71.15 plus 360 equals 431 comma 15 space open parentheses TM close parentheses end cell end table 

Dengan demikian,

HP={71,15;168,85;251,15;348,85}.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Acfreelance

Terakhir diupdate 13 September 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 yang serupa

Hasil penjumlahan dari semua anggota himpunan penyelesaian persamaan  untuk  adalah...

Pembahasan Soal:

Dengan menggunakan rumus trigonometri, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space open parentheses 3 x minus 15 close parentheses degree plus sin open parentheses 3 x minus 45 close parentheses degree end cell equals 0 row cell 2 sin open parentheses fraction numerator 3 x minus 15 plus 3 x minus 45 over denominator 2 end fraction close parentheses sin open parentheses fraction numerator 3 x minus 15 minus 3 x plus 45 over denominator 2 end fraction close parentheses end cell equals 0 row cell 2 sin open parentheses 3 x minus 30 close parentheses sin open parentheses 15 close parentheses end cell equals 0 row cell sin open parentheses 3 x minus 30 close parentheses end cell equals 0 end table

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell sin left parenthesis 3 x minus 30 right parenthesis end cell equals 0 row cell sin left parenthesis 3 x minus 30 right parenthesis end cell equals cell sin space 0 degree end cell row cell 3 x minus 30 degree end cell equals cell space 0 degree plus n times 360 degree end cell row cell 3 x end cell equals cell 30 degree plus n times 360 degree end cell row x equals cell 10 degree plus n times 120 degree end cell row cell untuk space n end cell equals cell 0 comma space 1 comma space 2 end cell row x equals cell 10 degree plus 0 times 120 degree end cell row blank equals cell 10 degree end cell row x equals cell 10 degree plus 1 times 120 degree end cell row blank equals cell 130 degree end cell row x equals cell 10 degree plus 2 times 120 degree end cell row blank equals cell 250 degree end cell row cell atau space 3 x minus 30 degree end cell equals cell space 180 degree plus n times 360 degree end cell row cell 3 x end cell equals cell 210 degree plus n times 360 degree end cell row x equals cell 70 degree plus n times 120 degree end cell row cell untuk space n end cell equals cell 0 comma space 1 comma space 2 end cell row x equals cell 70 degree plus 0 times 120 degree end cell row blank equals cell 70 degree end cell row x equals cell 70 degree plus 1 times 120 degree end cell row blank equals cell 190 degree end cell row x equals cell 70 degree plus 2 times 120 degree end cell row blank equals cell 310 degree end cell end table

Dengan demikian,

table attributes columnalign right center left columnspacing 0px end attributes row HP equals cell open curly brackets 10 degree comma space 70 degree comma space 130 degree comma space 190 degree comma space 250 degree comma space 310 degree close curly brackets end cell row cell Hasil space penjumlahan end cell equals cell 10 degree plus 70 degree plus 130 degree plus 190 degree plus 250 degree plus 310 degree end cell row blank equals cell 960 degree end cell end table


Oleh karena itu, tidak ada opsi jawaban yang benar.

0

Roboguru

Tentukan himpunan penyelesaian setiap persamaan berikut untuk . h.

Pembahasan Soal:

Terlebih dahulu kita ubah fungsi trigonometri tersebut sebagai berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space open parentheses 3 x minus 30 degree close parentheses end cell equals cell negative 1 half end cell row cell sin space open parentheses 3 x minus 30 degree close parentheses end cell equals cell sin space 210 degree end cell end table 

Berdasarkan rumus dasar trigonometri untuk sinus yaitu:

begin mathsize 12px style sin space x equals sin space A left right double arrow x equals A plus k times 360 space atau space x equals open parentheses 180 minus A close parentheses plus k times 360 end style 

Maka dapat dituliskan:

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 x minus 30 degree end cell equals cell 210 degree plus k times 360 degree end cell row cell 3 x end cell equals cell 210 degree plus 30 degree plus k times 360 degree end cell row cell 3 x end cell equals cell 240 degree plus k times 360 degree end cell row x equals cell fraction numerator 240 degree plus k times 360 degree over denominator 3 end fraction end cell row x equals cell 80 degree plus k times 120 degree end cell row blank blank blank end table 

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 x minus 30 degree end cell equals cell open parentheses 180 degree minus 210 degree close parentheses plus k times 360 degree end cell row cell 3 x minus 30 degree end cell equals cell negative 30 degree plus k times 360 degree end cell row cell 3 x end cell equals cell negative 30 degree plus 30 degree plus k times 360 degree end cell row cell 3 x end cell equals cell k times 360 degree end cell row x equals cell fraction numerator k times 360 degree over denominator 3 end fraction end cell row x equals cell k times 120 degree end cell end table 

Sehingga diperoleh:

table row cell n equals 0 end cell rightwards double arrow cell x subscript 1 equals 80 plus 0 equals 80 end cell row blank blank cell x subscript 2 equals open parentheses 0 close parentheses open parentheses 120 close parentheses equals 0 end cell row cell k equals 1 end cell rightwards double arrow cell x subscript 3 equals 80 plus 120 equals 200 end cell row blank blank cell x subscript 4 equals open parentheses 1 close parentheses open parentheses 120 close parentheses equals 120 end cell row cell k equals 2 end cell rightwards double arrow cell x subscript 5 equals 80 plus 240 equals 320 end cell row blank blank cell x subscript 6 equals open parentheses 2 close parentheses open parentheses 120 close parentheses equals 240 end cell row cell k equals 3 end cell rightwards double arrow cell x subscript 7 equals 80 plus 360 equals 440 space open parentheses TM close parentheses end cell row space blank cell x subscript 8 equals open parentheses 3 close parentheses open parentheses 120 close parentheses equals 360 end cell end table 

Dengan demikian,

HP = open curly brackets 0 degree comma space 80 degree comma space 120 degree comma space 200 degree comma space 240 degree comma space 320 degree comma space 360 degree close curly brackets

0

Roboguru

Himpunan penyelesaian dari persamaan sin 4x - cos 2x = 0 untuk  adalah. .. .

Pembahasan Soal:

c

Kemungkinan I.

Penyelesaian :

 

Kemungkinan II.

Penyelesaian :

jadi himpunan penyelesaiannya adalah

0

Roboguru

7. Tentukan himpunan penyelesaian setiap persamaan berikut untuk . d.

Pembahasan Soal:

Terlebih dahulu kita ubah fungsi trigonometri tersebut sebagai berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space open parentheses 2 x minus 150 degree close parentheses end cell equals cell negative 1 half square root of 2 end cell row cell sin space open parentheses 2 x minus 150 degree close parentheses end cell equals cell sin space 225 degree end cell end table 

Berdasarkan rumus dasar trigonometri untuk sinus yaitu:

sin space x equals sin space A left right double arrow x equals A plus n times 360 space atau space x equals open parentheses 180 minus A close parentheses plus n times 360 

Maka dapat dituliskan:

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x minus 150 degree end cell equals cell 225 degree plus n times 360 degree end cell row cell 2 x end cell equals cell 225 degree plus 150 degree plus n times 360 degree end cell row cell 2 x end cell equals cell 375 degree plus n times 360 degree end cell row x equals cell fraction numerator 375 degree plus n times 360 degree over denominator 2 end fraction end cell row x equals cell 187 comma 5 degree plus n times 180 end cell end table 

 

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x minus 150 degree end cell equals cell open parentheses 180 minus 225 close parentheses degree plus n times 360 degree end cell row cell 2 x minus 150 degree end cell equals cell negative 45 degree plus n times 360 degree end cell row cell 2 x end cell equals cell negative 45 degree plus 150 degree plus n times 360 degree end cell row cell 2 x end cell equals cell 105 degree plus n times 360 degree end cell row x equals cell fraction numerator 105 degree plus n times 360 degree over denominator 2 end fraction end cell row x equals cell 52 comma 5 degree plus n times 180 degree end cell end table 

Sehingga diperoleh:

table row cell n equals negative 3 end cell rightwards double arrow cell x subscript 1 equals 187 comma 5 minus 540 equals negative 352 comma 5 end cell row blank blank cell x subscript 2 equals 52 comma 5 minus 540 equals negative 487 comma 5 space open parentheses TM close parentheses end cell row cell n equals negative 2 end cell rightwards double arrow cell x subscript 3 equals 187 comma 5 minus 360 equals negative 172 comma 5 end cell row blank blank cell x subscript 4 equals 52 comma 5 minus 360 equals negative 307 comma 5 end cell row cell n equals negative 1 end cell rightwards double arrow cell x subscript 5 equals 187 comma 5 minus 180 equals 7 comma 5 end cell row blank blank cell x subscript 6 equals 52 comma 5 minus 180 equals negative 127 comma 5 end cell row cell n equals 0 end cell rightwards double arrow cell x subscript 7 equals 187 comma 5 plus 0 equals 187 comma 5 end cell row blank blank cell x subscript 8 equals 52 comma 5 plus 0 equals 52 comma 5 end cell row cell n equals 1 end cell rightwards double arrow cell x subscript 9 equals 187 comma 5 plus 180 equals 367 comma 5 space open parentheses TM close parentheses end cell row blank blank cell x subscript 10 equals 52 comma 5 plus 180 equals 232 comma 5 end cell end table  

Dengan demikian,

HP = {352,5;307,5;172,5;127,5}{7,5;52,5;187,5;232,5}

0

Roboguru

Himpunan penyelesaian dari persamaan  untuk  adalah...

Pembahasan Soal:

Ingat!

sinα+sinβ=2sin(2α+β)cos(2αβ) 

dan 

sinxx1x2===sinαα+k360(180α)+k360 
 

Dengan menggunakan rumus trigonometri, diperoleh:

sin(x+30)+sin(x120)2sin(2x+30+x120)cos(2x+30x+120)2sin(x45)cos75sin(x45)sin(x45)=====0000sin0

Maka 

x145x1x245x2x2=====0+k36045+k360(1800)+k360180+45+k360225+k360 

Untuk k=0, maka:

x1x2==45+0360=45225+0360=225

Untuk k=1, maka:

x1x2==45+1360=405225+1360=585Tidak Memenuhi 

Dengan demikian,

HP equals open curly brackets 45 degree comma space 225 degree close curly brackets


Oleh karena itu, jawaban yang benar adalah B.

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