Iklan

Iklan

Pertanyaan

Jika θ berada di kuadran kedua dengan tan θ = − 3 2 ​ . Tunjukkan bahwa: sin ( 27 0 ∘ + θ ) − cot ( − θ ) tan ( 9 0 ∘ − θ ) + cos ( 18 0 ∘ − θ ) ​ = 2 − 13 ​ 2 + 13 ​ ​

Jika  berada di kuadran kedua dengan . Tunjukkan bahwa:

Iklan

S. Nur

Master Teacher

Jawaban terverifikasi

Jawaban

tidak terbukti bahwa adalah .

tidak terbukti bahwa fraction numerator tan space open parentheses 90 degree minus theta close parentheses plus cos space open parentheses 180 degree minus theta close parentheses over denominator sin space open parentheses 270 degree plus theta close parentheses minus cot space open parentheses negative theta close parentheses end fraction adalah fraction numerator 2 plus square root of 13 over denominator 2 minus square root of 13 end fraction.

Iklan

Pembahasan

Ingat kembali perbandingan trigonometri sudut berelasi berikut. Jika , berada di kuadran II. Maka, Sehingga, diperoleh perhitungan: Jadi, tidak terbukti bahwa adalah .

Ingat kembali perbandingan trigonometri sudut berelasi berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space open parentheses 90 degree minus theta close parentheses end cell equals cell cot space theta end cell row cell sin space open parentheses 270 degree plus theta close parentheses end cell equals cell negative cos space theta end cell row cell cos space open parentheses 180 degree minus theta close parentheses end cell equals cell negative cos space theta end cell end table

Jika tan space theta equals negative 2 over 3theta berada di kuadran II.

tan space theta equals negative 2 over 3 equals de over sa

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell square root of 3 squared plus 2 squared end root end cell row blank equals cell square root of 9 plus 4 end root end cell row blank equals cell square root of 13 end cell end table

Maka, 

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space theta end cell equals cell de over mi equals fraction numerator 2 over denominator square root of 13 end fraction end cell row cell cos space theta end cell equals cell sa over mi equals negative fraction numerator 3 over denominator square root of 13 end fraction end cell end table

Sehingga, diperoleh perhitungan:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator tan space open parentheses 90 degree minus theta close parentheses plus cos space open parentheses 180 degree minus theta close parentheses over denominator sin space open parentheses 270 degree plus theta close parentheses minus cot space open parentheses negative theta close parentheses end fraction end cell equals cell fraction numerator 2 plus square root of 13 over denominator 2 minus square root of 13 end fraction end cell row cell fraction numerator cot space theta minus cos space theta over denominator negative space cos plus cot space theta end fraction end cell equals cell fraction numerator 2 plus square root of 13 over denominator 2 minus square root of 13 end fraction end cell row cell fraction numerator cot space theta minus cos space theta over denominator cot space theta minus space cos end fraction end cell equals cell fraction numerator 2 plus square root of 13 over denominator 2 minus square root of 13 end fraction end cell row 1 equals cell fraction numerator 2 plus square root of 13 over denominator 2 minus square root of 13 end fraction open parentheses Tidak space terbukti close parentheses end cell end table

Jadi, tidak terbukti bahwa fraction numerator tan space open parentheses 90 degree minus theta close parentheses plus cos space open parentheses 180 degree minus theta close parentheses over denominator sin space open parentheses 270 degree plus theta close parentheses minus cot space open parentheses negative theta close parentheses end fraction adalah fraction numerator 2 plus square root of 13 over denominator 2 minus square root of 13 end fraction.

171

Iklan

Iklan

Pertanyaan serupa

Jika θ berada di kuadran kedua dengan tan θ = − 3 2 ​ . Tunjukkan bahwa: cos ( 27 0 ∘ + θ ) + cos ( 36 0 ∘ − θ ) sin ( 9 0 ∘ − θ ) − cos ( 18 0 ∘ − θ ) ​ = 6

206

4.0

Jawaban terverifikasi

Iklan

Iklan

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

Fitur Roboguru

Topik Roboguru

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