Pergunakan formula sudut paruh untuk menghitung nilai dari ekspresi di bawah ini: a. sin (8π​) b. cos (8π​) c. tan (8π​)

Pertanyaan

Pergunakan formula sudut paruh untuk menghitung nilai dari ekspresi di bawah ini:

a. sin space open parentheses pi over 8 close parentheses

b. cos space open parentheses pi over 8 close parentheses

c. tan space open parentheses straight pi over 8 close parentheses

M. Nasrullah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Pembahasan

Ingat kembali:

-rumus sudut paruh:

sin space 1 half alpha equals plus-or-minus square root of fraction numerator 1 minus cos space alpha over denominator 2 end fraction end root cos space 1 half alpha equals plus-or-minus square root of fraction numerator 1 plus cos space alpha over denominator 2 end fraction end root tan space 1 half alpha equals fraction numerator sin space alpha over denominator 1 plus cos space alpha end fraction

-merasionalkan bentuk akar:

fraction numerator 1 over denominator a plus square root of b end fraction equals fraction numerator 1 over denominator a plus square root of b end fraction cross times fraction numerator a minus square root of b over denominator a minus square root of b end fraction

Sehingga diperoleh perhitungan:

a. sin space open parentheses pi over 8 close parentheses

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space open parentheses pi over 8 close parentheses end cell equals cell sin space open parentheses 180 over 8 close parentheses end cell row blank equals cell sin space open parentheses 45 over 2 close parentheses end cell row blank equals cell plus-or-minus square root of fraction numerator 1 minus cos space 45 over denominator 2 end fraction end root end cell row blank equals cell plus-or-minus square root of fraction numerator 1 minus begin display style fraction numerator square root of 2 over denominator 2 end fraction end style over denominator 2 end fraction end root end cell row blank equals cell plus-or-minus square root of fraction numerator 2 minus square root of 2 over denominator 4 end fraction end root end cell row cell sin space open parentheses pi over 8 close parentheses end cell equals cell fraction numerator square root of 2 minus square root of 2 end root over denominator 2 end fraction space atau space minus fraction numerator square root of 2 minus square root of 2 end root over denominator 2 end fraction end cell end table

b. cos space open parentheses pi over 8 close parentheses

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space open parentheses pi over 8 close parentheses end cell equals cell cos space open parentheses 180 over 8 close parentheses end cell row blank equals cell cos space open parentheses 45 over 2 close parentheses end cell row blank equals cell plus-or-minus square root of fraction numerator 1 plus cos space 45 over denominator 2 end fraction end root end cell row blank equals cell plus-or-minus square root of fraction numerator 1 plus begin display style fraction numerator square root of 2 over denominator 2 end fraction end style over denominator 2 end fraction end root end cell row blank equals cell plus-or-minus square root of fraction numerator 2 plus square root of 2 over denominator 4 end fraction end root end cell row cell cos space open parentheses pi over 8 close parentheses end cell equals cell fraction numerator square root of 2 plus square root of 2 end root over denominator 2 end fraction space atau space minus fraction numerator square root of 2 plus square root of 2 end root over denominator 2 end fraction end cell end table

c. tan space open parentheses straight pi over 8 close parentheses

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space open parentheses pi over 8 close parentheses end cell equals cell tan space open parentheses 180 over 8 close parentheses end cell row blank equals cell tan space open parentheses 45 over 2 close parentheses end cell row blank equals cell fraction numerator sin space 45 over denominator 1 plus cos space 45 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator square root of 2 over denominator 2 end fraction end style over denominator 1 plus begin display style fraction numerator square root of 2 over denominator 2 end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator square root of 2 over denominator up diagonal strike 2 end fraction end style over denominator begin display style fraction numerator 2 plus square root of 2 over denominator up diagonal strike 2 end fraction end style end fraction end cell row blank equals cell fraction numerator square root of 2 over denominator 2 plus square root of 2 end fraction cross times fraction numerator 2 minus square root of 2 over denominator 2 minus square root of 2 end fraction end cell row blank equals cell fraction numerator blank over denominator 4 minus 2 end fraction end cell row blank equals cell fraction numerator 2 square root of 2 minus 2 over denominator 2 end fraction end cell end table

Dengan demikian, dengan menggunakan formula sudut paruh, maka hasil dari:

sin space open parentheses pi over 8 close parentheses equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 2 minus square root of 2 end root over denominator 2 end fraction 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 atau 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 minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 2 minus square root of 2 end root over denominator 2 end fraction end cell end table

cos space open parentheses pi over 8 close parentheses equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 2 plus square root of 2 end root over denominator 2 end fraction 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 atau 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 minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 2 plus square root of 2 end root over denominator 2 end fraction end cell end table 

tan space open parentheses straight pi over 8 close parentheses equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 square root of 2 minus 2 over denominator 2 end fraction end cell end table

10

0.0 (0 rating)

Pertanyaan serupa

Tunjukkan bahwa: tan 2x​=±1+ cos x1−cos x​​

55

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

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