Roboguru

Jika sinα=51​5​, pernyataan di bawah ini yang benar adalah ....

Pertanyaan

Jika , pernyataan di bawah ini yang benar adalah .... 

  1.  

  2.  

  3.  

  4.  

  5.  

Pembahasan Soal:

 

Jika begin mathsize 14px style sin alpha equals y over r equals 1 fifth square root of 5 end style  maka,

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row x equals cell square root of r squared minus y squared end root end cell row blank equals cell square root of 5 squared minus left parenthesis square root of 5 right parenthesis squared end root end cell row blank equals cell square root of 25 minus 5 end root end cell row blank equals cell square root of 20 end cell row blank equals cell square root of 4 times 5 end root end cell row blank equals cell 2 square root of 5 end cell end table end style 

begin mathsize 14px style cos left parenthesis 90 degree plus alpha right parenthesis equals negative sin alpha equals negative 1 fifth square root of 5 end style 

undefined 

size 14px sin size 14px left parenthesis size 14px 90 size 14px degree size 14px plus size 14px alpha size 14px right parenthesis size 14px equals size 14px cos size 14px alpha size 14px equals size 14px 2 over size 14px 5 square root of size 14px 5 

undefined 

begin mathsize 14px style cos left parenthesis 180 degree plus alpha right parenthesis equals negative cos alpha equals negative 2 over 5 square root of 5 end style  

Jadi,  pernyataan yang benar adalah A 

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Acfreelance

Terakhir diupdate 05 Oktober 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

cos225∘⋅sin45∘⋅cotan250∘sin300∘⋅cos50∘⋅tan160∘​=...

Pembahasan Soal:

Dengan menggunakan rumus sudut berelasi, diperoleh 

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator sin space 300 degree times cos space 50 degree times tan space 160 degree over denominator cos space 225 degree times sin space 40 degree times cotan space 250 degree end fraction end cell row blank equals cell fraction numerator sin space 300 degree times cos space open parentheses 90 minus 40 close parentheses degree times tan space open parentheses 90 plus 70 close parentheses degree over denominator cos space 225 degree times sin space 40 degree times cotan space open parentheses 180 plus 70 close parentheses degree end fraction end cell row blank equals cell fraction numerator sin space 300 degree times sin space 40 degree times open parentheses negative cotan space 70 degree close parentheses over denominator cos space 225 degree times sin space 40 degree times cotan space 70 degree end fraction end cell row blank equals cell negative fraction numerator sin space 300 degree over denominator cos space 225 end fraction end cell row blank equals cell negative fraction numerator negative begin display style 1 half end style square root of 3 over denominator negative begin display style 1 half end style square root of 2 end fraction end cell row blank equals cell negative fraction numerator square root of 3 over denominator square root of 2 end fraction end cell row blank equals cell negative 1 half square root of 3 end cell end table 

Jadi,  fraction numerator sin space 300 degree times cos space 50 degree times tan space 160 degree over denominator cos space 225 degree times sin space 45 degree times cotan space 250 degree end fraction equals negative 1 half square root of 3

0

Roboguru

Bentuk sederhana dari cosec(180∘+x)tan(90∘−x)cot(90∘+x)sec(270∘−x)​ adalah ....

Pembahasan Soal:

Perhatikan perhitungan berikut!

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator cot left parenthesis 90 degree plus x right parenthesis sec left parenthesis 270 degree minus x right parenthesis over denominator cosec left parenthesis 180 degree plus x right parenthesis tan left parenthesis 90 degree minus x right parenthesis end fraction end cell row blank equals cell fraction numerator left parenthesis negative tan x right parenthesis left parenthesis negative cosec x right parenthesis over denominator left parenthesis negative cosec x right parenthesis left parenthesis cot x right parenthesis end fraction end cell row blank equals cell fraction numerator negative tan x over denominator cot x end fraction end cell row blank equals cell fraction numerator negative tan x over denominator begin display style fraction numerator 1 over denominator tan x end fraction end style end fraction end cell row blank equals cell negative tan x times tan x end cell row blank equals cell negative tan squared x end cell end table end style

Jadi, jawaban yang tepat adalah C.

0

Roboguru

Hitunglah nilai dari tan(−45∘)−2(tan855∘)sin(−120∘)+cos(−510∘)​= ...

Pembahasan Soal:

Diketahui:

Operasi sudut trigonometri.

Ingatlah kembali rumus Perbandingan trigonometri Sudut-sudut Berelasi, yaitu:

begin mathsize 14px style table attributes columnalign left center right end attributes row cell sin open parentheses 90 degree minus alpha close parentheses end cell equals cell cos space alpha end cell row cell cos open parentheses 90 degree minus alpha close parentheses end cell equals cell sin space alpha end cell row cell tan open parentheses 90 degree minus alpha close parentheses end cell equals cell cot space alpha end cell row cell cot open parentheses 90 degree plus alpha close parentheses end cell equals cell negative tan space alpha end cell row cell tan open parentheses 180 degree minus alpha close parentheses end cell equals cell negative tan space alpha end cell row cell cos open parentheses 180 degree plus alpha close parentheses end cell equals cell negative cos space alpha end cell row cell sin open parentheses 270 degree minus alpha close parentheses end cell equals cell negative cos space alpha end cell row cell sin open parentheses 360 degree plus alpha close parentheses end cell equals cell sin space alpha end cell row cell tan open parentheses 360 degree plus alpha close parentheses end cell equals cell tan space alpha end cell end table end style

Sehingga diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin open parentheses negative 120 degree close parentheses end cell equals cell sin open parentheses 90 degree minus 210 degree close parentheses end cell row blank equals cell cos space 210 degree end cell row cell cos space 210 degree end cell equals cell cos open parentheses 180 degree plus 30 degree close parentheses end cell row blank equals cell negative cos space 30 degree end cell row blank equals cell negative 1 half square root of 3 end cell row blank blank blank row cell cos open parentheses negative 510 degree close parentheses end cell equals cell cos open parentheses 90 degree minus 600 degree close parentheses end cell row blank equals cell sin space 600 degree end cell row cell sin space 600 degree end cell equals cell sin space open parentheses 360 degree plus 240 degree close parentheses end cell row blank equals cell sin space 240 degree end cell row cell sin space 240 degree end cell equals cell sin open parentheses 270 degree minus 30 degree close parentheses end cell row blank equals cell negative cos space 30 degree end cell row blank equals cell negative 1 half square root of 3 end cell row blank blank blank row cell tan open parentheses negative 45 degree close parentheses end cell equals cell tan open parentheses 90 degree minus 135 degree close parentheses end cell row blank equals cell cot space 135 degree end cell row cell cot space 135 degree end cell equals cell cot open parentheses 90 degree plus 45 degree close parentheses end cell row blank equals cell negative tan space 45 degree end cell row blank equals cell negative 1 end cell row blank blank blank row cell tan space 855 degree end cell equals cell tan open parentheses 360 degree plus 495 degree close parentheses end cell row blank equals cell tan space 495 degree end cell row cell tan space 495 degree end cell equals cell tan open parentheses 360 degree plus 135 degree close parentheses end cell row blank equals cell tan space 135 degree end cell row cell tan space 135 degree end cell equals cell tan open parentheses 180 degree minus 45 degree close parentheses end cell row blank equals cell negative tan space 45 degree end cell row blank equals cell negative 1 end cell end table end style

 Kemudian operasikan sudut-sudut trigonometrinya seperti berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sin open parentheses negative 120 degree close parentheses plus cos open parentheses negative 510 degree close parentheses over denominator tan open parentheses negative 45 degree close parentheses minus 2 open parentheses tan space 855 degree close parentheses end fraction end cell equals cell fraction numerator negative begin display style 1 half end style square root of 3 plus open parentheses negative 1 half square root of 3 close parentheses over denominator negative 1 minus open parentheses 2 open parentheses negative 1 close parentheses close parentheses end fraction end cell row blank equals cell fraction numerator negative begin display style 1 half end style square root of 3 minus 1 half square root of 3 over denominator negative 1 minus open parentheses negative 2 close parentheses end fraction end cell row blank equals cell fraction numerator negative begin display style 2 over 2 end style square root of 3 over denominator negative 1 plus 2 end fraction end cell row blank equals cell fraction numerator negative square root of 3 over denominator 1 end fraction end cell row blank equals cell negative square root of 3 end cell end table end style

Maka, nilai dari begin mathsize 14px style fraction numerator sin space open parentheses negative 120 degree close parentheses plus cos space open parentheses negative 510 degree close parentheses over denominator tan space open parentheses negative 45 degree close parentheses minus 2 space open parentheses tan space 855 degree close parentheses end fraction equals end stylebegin mathsize 14px style negative square root of 3 end style.

0

Roboguru

Nyatakan dalam bentuk yang paling sederhana. b. cos(90∘+A)+sin(180∘−A)−sin(180∘+A)−sin(−A).

Pembahasan Soal:

Ingat!

cos(90+α)=sin(α)sin(180α)=sin(α)sin(180+α)=sin(α)sin(α)=sin(α) 

Gunakan rumus sudut berelasi, sehingga diperoleh sebagai berikut:

cos(90+A)+sin(180A)sin(180+A)sin(A)=sinA+sinA(sinA)(sinA)=sinA+sinA=2sinA  

Jadi, diperoleh bentuk paling sederhananya adalah begin mathsize 14px style 2 space sin space straight A end style.

0

Roboguru

Nyatakan dalam bentuk yang paling sederhana. a. tan(180∘+A)sin(90∘−A)sec(90∘−A)

Pembahasan Soal:

Gunakan rumus sudut berelasi, diperoleh perhitungan berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell tan space open parentheses 180 degree plus straight A close parentheses times sin space open parentheses 90 degree minus straight A close parentheses times sec space open parentheses 90 degree minus straight A close parentheses end cell equals cell tan space straight A times cos space straight A times cosec space straight A end cell row blank equals cell tan space straight A times cos space straight A times fraction numerator 1 over denominator cos space straight A end fraction end cell row blank equals cell tan space straight A end cell end table end style 

Jadi, bentuk sederhananya adalah begin mathsize 14px style tan space straight A end style.

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