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Pertanyaan

cotan space 300 degree plus sin space 315 degree minus sign cos space 225 degree equals horizontal ellipsis 

Pembahasan Soal:

Operasi penjumlahan pada fungsi trigonometri di atas dapat dihitung seperti berikut,

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell cotan space 300 degree plus sin space 315 degree minus cos space 225 degree end cell row blank equals cell fraction numerator 1 over denominator tan left parenthesis 360 degree minus 60 degree right parenthesis end fraction plus sin left parenthesis 360 degree minus 315 degree right parenthesis end cell row blank blank cell negative cos left parenthesis 180 degree plus 45 degree right parenthesis end cell row blank equals cell fraction numerator 1 over denominator negative tan space 60 degree end fraction plus open parentheses sin space 45 degree close parentheses minus open parentheses negative cos space 45 degree close parentheses end cell row blank equals cell negative fraction numerator 1 over denominator square root of 3 end fraction plus fraction numerator square root of 2 over denominator 2 end fraction plus fraction numerator square root of 2 over denominator 2 end fraction end cell row blank equals cell square root of 2 minus 1 third square root of 3 end cell end table 

Jadi, hasil dari operasi tersebut adalah square root of 2 minus 1 third square root of 3.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

I. Kumaralalita

Mahasiswa/Alumni Universitas Gadjah Mada

Terakhir diupdate 06 Juni 2021

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Pertanyaan yang serupa

Tentukan hasil dari .

Pembahasan Soal:

Ingatlah aturan perbandingan trigonometri sudut berelasi

cos space open parentheses 180 degree plus alpha close parentheses equals negative cos space alpha

dan

sin space open parentheses 360 degree minus alpha close parentheses equals negative sin space alpha.

Maka

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space 240 degree end cell equals cell cos space open parentheses 180 degree plus 60 degree close parentheses end cell row blank equals cell negative cos space 60 degree end cell row blank equals cell negative 1 half end cell end table

dan

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 300 degree end cell equals cell sin space open parentheses 360 degree minus 60 degree close parentheses end cell row blank equals cell negative sin space 60 degree end cell row blank equals cell negative 1 half square root of 3 end cell end table

Dengan demikian,

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space 240 degree minus sin space 300 degree end cell equals cell negative 1 half minus open parentheses negative 1 half square root of 3 close parentheses end cell row blank equals cell negative 1 half plus 1 half square root of 3 end cell row blank equals cell 1 half open parentheses square root of 3 minus 1 close parentheses end cell end table

Jadi, hasil dari cos space 240 degree minus sin space 300 degree adalah 1 half open parentheses square root of 3 minus 1 close parentheses.

Roboguru

Tentukan nilai dari:

Pembahasan Soal:

Gunakanlah sudut berelasi untuk menjawab soal di atas.

Ingat!

  • Nilai sin pada kuadran II adalah positif, sedangkan nilai cos dan tan negatif.
  • Nilai tan pada kuadran III positif, sedangkan nilai sin dan cos negatif.
  • Nilai cos  pada kuadran IV positif, sedangkan nilai sin dan tan negatif.

Berdasarkan nilai trigonometri pada kuadran II, III, dan IV di atas, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sin space 300 degree space tan space 330 degree space sec space 420 degree over denominator cot space 135 degree space cos space 210 degree space csc space 315 degree end fraction end cell equals cell fraction numerator sin space 300 degree space tan space 330 degree space begin display style fraction numerator 1 over denominator cos space 420 degree end fraction end style over denominator begin display style fraction numerator 1 over denominator tan space 135 degree end fraction end style space cos space 210 degree space begin display style fraction numerator 1 over denominator sin space 315 degree end fraction end style end fraction end cell row blank equals cell fraction numerator sin space 300 degree space tan space 330 degree space tan space 135 degree space sin space 315 degree over denominator begin display style cos space 210 degree space cos space 420 degree end style end fraction end cell row blank equals cell fraction numerator sin open parentheses 360 degree minus 60 degree close parentheses times tan open parentheses 360 degree minus 30 degree close parentheses times begin display style tan open parentheses 180 degree minus 45 degree close parentheses times sin open parentheses 360 degree minus 45 degree close parentheses end style over denominator begin display style cos open parentheses 1 times 360 degree plus 60 degree close parentheses end style times cos open parentheses 180 degree plus 30 degree close parentheses end fraction end cell row blank equals cell fraction numerator negative sin space 60 degree times open parentheses negative tan space 30 degree close parentheses times open parentheses negative tan space 45 degree close parentheses times open parentheses negative sin space 45 degree close parentheses over denominator cos space 60 degree times open parentheses negative cos space 30 degree close parentheses end fraction end cell row blank equals cell fraction numerator negative begin display style fraction numerator square root of 3 over denominator 2 end fraction end style times open parentheses negative begin display style fraction numerator square root of 3 over denominator 3 end fraction end style close parentheses times open parentheses negative 1 close parentheses times open parentheses negative begin display style fraction numerator square root of 2 over denominator 2 end fraction end style close parentheses over denominator begin display style 1 half end style times open parentheses negative begin display style fraction numerator square root of 3 over denominator 2 end fraction end style close parentheses end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 3 square root of 2 over denominator 4 times 3 end fraction end style over denominator negative begin display style fraction numerator square root of 3 over denominator 4 end fraction end style end fraction end cell row blank equals cell negative fraction numerator square root of 2 over denominator 4 end fraction times fraction numerator 4 over denominator square root of 3 end fraction end cell row blank equals cell negative fraction numerator square root of 2 over denominator square root of 3 end fraction cross times fraction numerator square root of 3 over denominator square root of 3 end fraction end cell row blank equals cell negative fraction numerator square root of 6 over denominator 3 end fraction. end cell end table    

Dengan demikian, nilai dari fraction numerator sin space 300 degree space tan space 330 degree space sec space 420 degree over denominator cot space 135 degree space cos space 210 degree space csc space 315 degree end fraction adalah 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 6 over denominator 3 end fraction end cell end table.

Roboguru

Tentukan nilai dari .

Pembahasan Soal:

Gunakanlah sudut berelasi untuk menjawab soal di atas.

Ingat!

  • Nilai sin pada kuadran II adalah positif, sedangkan nilai cos dan tan negatif.
  • Nilai tan pada kuadran III positif, sedangkan nilai sin dan cos negatif.
  • Nilai cos  pada kuadran IV positif, sedangkan nilai sin dan tan negatif.

Berdasarkan nilai trigonometri pada kuadran II, III, dan IV di atas, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sin space 150 degree plus sin space 120 degree over denominator cos space 210 degree minus cos space 300 degree end fraction end cell equals cell fraction numerator sin open parentheses 180 degree minus 30 degree close parentheses plus sin open parentheses 180 degree minus 60 degree close parentheses over denominator cos open parentheses 180 degree plus 30 degree close parentheses minus cos open parentheses 360 degree minus 60 degree close parentheses end fraction end cell row blank equals cell fraction numerator sin space 30 degree plus sin space 60 degree over denominator negative cos space 30 degree minus cos space 60 degree end fraction end cell row blank equals cell fraction numerator begin display style 1 half end style plus begin display style fraction numerator square root of 3 over denominator 2 end fraction end style over denominator negative begin display style fraction numerator square root of 3 over denominator 2 end fraction end style minus begin display style 1 half end style end fraction end cell row blank equals cell fraction numerator begin display style 1 half plus fraction numerator square root of 3 over denominator 2 end fraction end style over denominator negative open parentheses begin display style 1 half end style plus begin display style fraction numerator square root of 3 over denominator 2 end fraction end style close parentheses end fraction end cell row blank equals cell negative 1. end cell end table  

Dengan demikian, nilai dari fraction numerator sin space 150 degree plus sin space 120 degree over denominator cos space 210 degree minus cos space 300 degree end fraction adalah negative 1.

Roboguru

Hasil dari  adalah ....

Pembahasan Soal:

Permasalahan di atas dapat diselesaikan dengan menggunakan relasi sudut trigonometri sebagai berikut:

begin mathsize 11px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell tan 120 degree space sin 150 degree minus cos 240 degree space sin 300 degree end cell row blank equals cell open parentheses tan open parentheses 180 degree minus 60 degree close parentheses sin open parentheses 180 degree minus 30 degree close parentheses close parentheses minus open parentheses cos open parentheses 180 degree plus 60 degree close parentheses sin open parentheses 360 degree minus 60 degree close parentheses close parentheses end cell row blank equals cell open parentheses negative tan 60 degree sin 30 degree close parentheses minus open parentheses open parentheses negative cos 60 degree close parentheses open parentheses negative sin 60 degree close parentheses close parentheses end cell row blank equals cell open parentheses negative square root of 3 cross times 1 half close parentheses minus open parentheses open parentheses negative 1 half close parentheses cross times open parentheses negative 1 half square root of 3 close parentheses close parentheses end cell row blank equals cell open parentheses negative 1 half square root of 3 close parentheses minus open parentheses 1 fourth square root of 3 close parentheses end cell row blank equals cell negative 2 over 4 square root of 3 minus 1 fourth square root of 3 end cell row blank equals cell negative 3 over 4 square root of 3 end cell end table end style 

Jadi, hasil dari tan 120 degree space sin 150 degree minus cos 240 degree space sin 300 degreeadalah negative 3 over 4 square root of 3.

Oleh karena itu, jawaban yang benar adalah A.space 

Roboguru

Nilai dari ....

Pembahasan Soal:

Dengan menerapkan rumus sudut-sudut berelasi dan nilai sudut istimewa, diperoleh perhitungan sebagai berikut.

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator sin space 60 degree cross times cos space 210 degree cross times tan space 330 degree over denominator 2 space sin space 30 degree cross times cos space 120 degree end fraction end cell row blank equals cell fraction numerator sin space 60 degree cross times cos space open parentheses 180 degree plus 30 degree close parentheses cross times tan space open parentheses 360 degree minus 30 degree close parentheses over denominator 2 space sin space 30 degree cross times cos space open parentheses 180 degree minus 60 degree close parentheses end fraction end cell row blank equals cell fraction numerator sin space 60 degree cross times open parentheses negative cos space 30 degree close parentheses cross times open parentheses negative tan space 30 degree close parentheses over denominator 2 space sin space 30 degree cross times open parentheses negative cos space 60 degree close parentheses end fraction end cell row blank equals cell fraction numerator up diagonal strike begin display style 1 half end style end strike square root of 3 cross times open parentheses negative up diagonal strike begin display style 1 half end style end strike square root of 3 close parentheses cross times open parentheses negative begin display style 1 third end style square root of 3 close parentheses over denominator 2 cross times up diagonal strike begin display style 1 half end style end strike cross times open parentheses negative up diagonal strike begin display style 1 half end style end strike close parentheses end fraction end cell row blank equals cell fraction numerator negative begin display style 1 third end style open parentheses 3 close parentheses over denominator negative 2 end fraction end cell row blank equals cell fraction numerator negative 1 over denominator negative 2 end fraction end cell row blank equals cell 1 half end cell end table end style 

Jadi, nilai dari fraction numerator sin space 60 degree cross times cos space 210 degree cross times tan space 330 degree over denominator 2 space sin space 30 degree cross times cos space 120 degree end fraction adalah 1 half.

Dengan demikian, jawaban yang tepat adalah B.

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