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sin150∘⋅cos225∘sin270∘⋅cos135∘⋅tan135∘​=…

Pertanyaan

fraction numerator sin space 270 degree middle dot cos space 135 degree middle dot tan space 135 degree over denominator sin space 150 degree middle dot cos space 225 degree end fraction equals horizontal ellipsis 

  1. infinity 

  2. 4 

  3. 2 

  4. 0 

  5. 1 

Pembahasan Soal:

Perkalian dan pembagian fungsi trigonometri di atas dapat diselesaikan dengan terlebih dahulu menghitung satu persatu nilai sudutnya. Sudut pada kuadran II yaitu ketika 90 degree less than x less or equal than 180 degree bernilai positif untuk fungsi sinus. Sudut pada kuadran III yaitu ketika 180 degree less than x less or equal than 270 degree bernilai positif untuk fungsi tangen.

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator sin space 270 degree times cos space 135 degree times tan space 135 degree over denominator sin space 150 degree times cos space 225 degree end fraction end cell row blank equals cell fraction numerator left parenthesis negative sin space 90 degree right parenthesis times left parenthesis negative cos space 45 degree right parenthesis times left parenthesis negative tan space 45 degree right parenthesis over denominator open parentheses sin space 30 degree close parentheses times left parenthesis negative cos space 45 degree right parenthesis end fraction end cell row blank equals cell fraction numerator left parenthesis negative 1 right parenthesis times open parentheses negative begin display style 1 half end style square root of 2 close parentheses open parentheses negative 1 close parentheses over denominator open parentheses begin display style 1 half end style close parentheses times open parentheses negative begin display style 1 half end style square root of 2 close parentheses end fraction end cell row blank equals cell fraction numerator negative begin display style 1 half end style up diagonal strike square root of 2 end strike over denominator negative begin display style 1 fourth end style up diagonal strike square root of 2 end strike end fraction end cell row blank equals cell negative 1 half times left parenthesis negative 4 right parenthesis end cell row blank equals 2 end table

Dengan demikian, hasil dari operasi di atas adalah 2.

Jadi, jawaban yang terbentuk adalah C.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

I. Kumaralalita

Mahasiswa/Alumni Universitas Gadjah Mada

Terakhir diupdate 06 Oktober 2021

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Pertanyaan yang serupa

Hitunglah hasil dari soal di bawah ini: sin150∘⋅cos225∘sin45∘⋅cos135∘⋅tan135∘​

Pembahasan Soal:

Ingat konsep nilai pada kuadran II dan III:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos space open parentheses 180 degree minus alpha close parentheses end cell equals cell negative cos space alpha end cell row cell sin space open parentheses 180 degree minus alpha close parentheses end cell equals cell sin space alpha end cell row cell tan space open parentheses 180 degree minus alpha close parentheses end cell equals cell negative tan space alpha end cell row cell cos space open parentheses 180 degree plus alpha close parentheses end cell equals cell negative cos space alpha end cell end table end style

Kemudian gunakan konsep tersebut sehingga:

 begin mathsize 14px style fraction numerator sin space 45 degree times cos space 135 degree times tan space 135 degree over denominator sin space 150 degree times cos space 225 degree end fraction equals fraction numerator sin space 45 degree times cos space open parentheses 180 degree minus 45 degree close parentheses times tan space open parentheses 180 degree minus 45 degree close parentheses over denominator sin space open parentheses 180 degree minus 30 degree close parentheses times cos space open parentheses 180 degree plus 45 degree close parentheses end fraction equals fraction numerator sin space 45 degree times open parentheses negative cos space 45 degree close parentheses times open parentheses negative tan space 45 degree close parentheses over denominator open parentheses sin space 30 degree close parentheses times open parentheses negative cos space 45 degree close parentheses end fraction equals fraction numerator begin display style 1 half end style square root of 2 times open parentheses negative 1 half square root of 2 close parentheses times open parentheses negative 1 close parentheses over denominator open parentheses begin display style 1 half end style close parentheses open parentheses negative begin display style 1 half end style square root of 2 close parentheses end fraction equals fraction numerator begin display style 1 fourth end style times 2 over denominator negative begin display style 1 fourth end style square root of 2 end fraction equals negative fraction numerator 2 over denominator square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction equals negative square root of 2 end style 

Dengan demikian nilai dari begin mathsize 14px style fraction numerator sin space 45 degree times cos space 135 degree times tan space 135 degree over denominator sin space 150 degree times cos space 225 degree end fraction end style adalah begin mathsize 14px style negative square root of 2 end style.

0

Roboguru

Nilai dari sin150∘+4⋅cos330∘−tg225∘

Pembahasan Soal:

Nilai sinus pada sudut berelasi di kuadran II, yaitu

sin space open parentheses 180 degree minus alpha close parentheses equals sin space alpha

Nilai tangen pada sudut berelasi di kuadran III, yaitu

tan space open parentheses 180 degree plus alpha close parentheses equals tan space alpha

Nilai cosinus pada sudut berelasi di kuadran IV, yaitu

cos space open parentheses 360 degree minus alpha close parentheses equals cos space alpha

Berdasarkan konsep di atas, dapat ditentukan nilai trigonometri dari berbagai kuadran berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 150 degree end cell equals cell sin space open parentheses 180 degree minus 30 degree close parentheses end cell row blank equals cell sin space 30 degree end cell row blank equals cell 1 half end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space 330 degree end cell equals cell cos space open parentheses 360 degree minus 30 degree close parentheses end cell row blank equals cell cos space 30 degree end cell row blank equals cell 1 half square root of 3 end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell t g space 225 degree end cell equals cell t g space open parentheses 180 degree plus 45 degree close parentheses end cell row blank equals cell t g space 45 degree end cell row blank equals 1 end table

Hasil dari operasi hitung nilai trigonometri tersebut adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell sin space 150 degree plus 4 times cos space 330 degree minus t g space 225 degree end cell row blank equals cell 1 half plus 4 times 1 half square root of 3 minus 1 end cell row blank equals cell 2 square root of 3 minus 1 half end cell end table

Dengan demikian, nilai table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin 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 150 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank degree end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos 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 330 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank degree 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 t end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank g 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 225 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank degree end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 3 end cell 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 1 half end cell end table 

0

Roboguru

cos210∘−cos300∘sin150∘+sin120∘​=…

Pembahasan Soal:

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 space open parentheses 90 degree plus 60 degree close parentheses plus sin space open parentheses 90 degree plus 30 degree close parentheses over denominator cos space open parentheses 180 degree plus 30 degree close parentheses minus cos space open parentheses 270 degree plus 30 degree close parentheses end fraction end cell row blank equals cell fraction numerator cos space 60 degree plus cos space 30 degree over denominator negative cos space 30 degree minus sin space 30 degree end fraction end cell row blank equals cell fraction numerator begin display style 1 half end style plus begin display style 1 half end style square root of 3 over denominator negative begin display style 1 half end style square root of 3 minus begin display style 1 half end style end fraction end cell row blank equals cell fraction numerator begin display style 1 half plus 1 half square root of 3 end style over denominator negative open parentheses begin display style 1 half end style square root of 3 plus begin display style 1 half end style close parentheses end fraction end cell row blank equals cell negative 1 end cell end table 

Jadi, fraction numerator sin space 150 degree plus sin space 120 degree over denominator cos space 210 degree minus cos space 300 degree end fraction equals negative 1.

0

Roboguru

Tentukan nilai dari cos210∘−cos300∘sin150∘+sin120∘​.

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.

0

Roboguru

Tentukan nilai dari sin150∘×cos225∘cos135∘×tan240∘×sin270∘​.

Pembahasan Soal:

Gunakanlah sudut berelasi untuk menjawab soal di atas. Nilai sin pada kuadran II adalah positif, sedangkan nilai cos dan tan negatif. Lalu, nilai tan pada kuadran III positif, sedangakan nilai sin dan cos negatif. Maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator cos space 135 degree cross times tan space 240 degree cross times sin space 270 degree over denominator sin space 150 degree cross times cos space 225 degree end fraction end cell equals cell fraction numerator cos open parentheses 180 degree minus 45 degree close parentheses cross times tan open parentheses 180 degree plus 60 degree close parentheses cross times sin open parentheses 180 degree plus 90 degree close parentheses over denominator sin open parentheses 180 degree minus 30 degree close parentheses cross times cos open parentheses 180 degree plus 45 degree close parentheses end fraction end cell row blank equals cell fraction numerator negative cos space 45 degree cross times tan space 60 degree cross times open parentheses negative sin space 90 degree close parentheses over denominator sin space 30 degree cross times open parentheses negative cos space 45 degree close parentheses end fraction end cell row blank equals cell fraction numerator negative begin display style fraction numerator square root of 2 over denominator 2 end fraction end style cross times square root of 3 cross times open parentheses negative 1 close parentheses over denominator begin display style 1 half end style cross times open parentheses negative begin display style fraction numerator square root of 2 over denominator 2 end fraction end style close parentheses end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator square root of 6 over denominator 2 end fraction end style over denominator negative begin display style fraction numerator square root of 2 over denominator 4 end fraction end style end fraction end cell row blank equals cell fraction numerator square root of 6 over denominator 2 end fraction cross times negative fraction numerator 4 over denominator square root of 2 end fraction end cell row blank equals cell negative 2 square root of 3. end cell end table 

Dengan demikian, nilai dari fraction numerator cos space 135 degree cross times tan space 240 degree cross times sin space 270 degree over denominator sin space 150 degree cross times cos space 225 degree end fraction adalah negative 2 square root of 3.

0

Roboguru

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