Roboguru

Pertanyaan

Jika tan space alpha equals 3 over 4 dan cos space beta equals 7 over 10 square root of 2, dengan alpha dan beta adalah sudut lancip maka alpha plus beta equals.... 

  1. fraction numerator 3 straight pi over denominator 4 end fraction 

  2. fraction numerator 2 straight pi over denominator 3 end fraction 

  3. straight pi over 2 

  4. straight pi over 3 

  5. straight pi over 4 

N. Puspita

Master Teacher

Jawaban terverifikasi

Pembahasan

Ingat kembali:

sin space straight A equals fraction numerator sisi space depan over denominator sisi space miring end fraction cos space straight A equals fraction numerator sisi space samping over denominator sisi space miring end fraction tan space straight A equals fraction numerator sisi space depan over denominator sisi space samping end fraction sin space open parentheses straight A plus straight B close parentheses equals sin space straight A times cos space straight B plus cos space straight A times sin space straight B cos space open parentheses straight A plus straight B close parentheses equals cosA times cos space straight B minus sin space straight A times sin space straight B tan space open parentheses straight A plus straight B close parentheses equals fraction numerator tan space straight A plus tan space straight B over denominator 1 minus tan space straight A times tan space straight B end fraction 

Jika tan space alpha equals 3 over 4 dan cos space beta equals 7 over 10 square root of 2, dengan alpha dan beta adalah sudut lancip maka dapat digambarkan sebagai berikut:

Dari gambar di atas dapat ditentukan:

- Nilai x 

x equals square root of 3 squared plus 4 squared end root x equals square root of 9 plus 16 end root x equals square root of 25 x equals 5 

- Nilai y 

y equals square root of 10 squared minus open parentheses 7 square root of 2 close parentheses squared end root y equals square root of 100 minus open parentheses 49 times 2 close parentheses end root y equals square root of 100 minus 98 end root y equals square root of 2 

Maka:

sin space alpha equals fraction numerator sisi space depan over denominator sisi space miring end fraction equals 3 over x equals 3 over 5 cos space alpha equals fraction numerator sisi space samping over denominator sisi space miring end fraction equals 4 over x equals 4 over 5 sin space beta equals fraction numerator sisi space depan over denominator sisi space miring end fraction equals y over 10 equals fraction numerator square root of 2 over denominator 10 end fraction tan space beta equals fraction numerator sisi space depan over denominator sisi space samping end fraction equals fraction numerator y over denominator 7 square root of 2 end fraction equals fraction numerator up diagonal strike square root of 2 end strike over denominator 7 up diagonal strike square root of 2 end strike end fraction equals 1 over 7 

Sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space open parentheses alpha plus beta close parentheses end cell equals cell sin space alpha times cos space beta plus cos space alpha times sin space beta end cell row blank equals cell 3 over 5 times 7 over 10 square root of 2 plus 4 over 5 times fraction numerator square root of 2 over denominator 10 end fraction end cell row blank equals cell 21 over 50 square root of 2 plus 4 over 50 square root of 2 end cell row blank equals cell 25 over 50 square root of 2 end cell row blank equals cell 1 half square root of 2 end cell row blank equals cell sin space 45 degree end cell end table 

Dengan demikian:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space open parentheses alpha plus beta close parentheses end cell equals cell sin space 45 degree end cell row cell open parentheses alpha plus beta close parentheses end cell equals cell 45 degree end cell row blank equals cell 45 degree cross times fraction numerator straight pi over denominator 180 degree end fraction end cell row blank equals cell fraction numerator 45 degree straight pi over denominator 180 degree end fraction end cell row blank equals cell straight pi over 4 end cell end table 

Jadi, jawaban yang benar adalah E.

28

0.0 (0 rating)

Pertanyaan serupa

Diketahui sinx=53​, dan cosy=1312​, x sudut tumpul dan y sudut lancip. Maka nilai dari  adalah …

58

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 Ruangguru

Produk Ruangguru

Produk Lainnya

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