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Hitunglah nilai dari

Pertanyaan

Hitunglah nilai dari fraction numerator sin space 270 degree times cos space 270 degree tan space 270 degree over denominator sin space 150 degree times cos space 225 degree end fraction

Pembahasan Soal:

Ingat konsep nilai dan sudut pada kuadran II dan III:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 270 degree end cell equals cell sin space open parentheses 180 degree plus 90 degree close parentheses end cell row blank equals cell negative sin space 90 degree end cell row blank equals cell negative 1 end cell row cell cos space 270 degree end cell equals cell cos space open parentheses 180 degree plus 90 degree close parentheses end cell row blank equals cell negative cos space 90 degree end cell row blank equals 0 row cell tan space 270 degree end cell equals cell tan space open parentheses 180 degree plus 90 degree close parentheses end cell row blank equals cell tan space 90 degree end cell row blank equals cell tak space terdefinisi end cell 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 row cell cos space 225 degree end cell equals cell cos space open parentheses 180 degree plus 45 degree close parentheses end cell row blank equals cell negative cos space 45 degree end cell row blank equals cell negative 1 half square root of 2 end cell end table

kemudian substitusikan sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sin space 270 degree times cos space 270 degree tan space 270 degree over denominator sin space 150 degree times cos space 225 degree end fraction end cell equals cell fraction numerator open parentheses negative 1 close parentheses open parentheses 0 close parentheses open parentheses tak space terdefinisi close parentheses over denominator begin display style 1 half end style 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 0 over denominator negative begin display style 1 fourth end style square root of 2 end fraction end cell row blank equals 0 end table 

Dengan demikian nilai dari fraction numerator sin space 270 degree times cos space 270 degree tan space 270 degree over denominator sin space 150 degree times cos space 225 degree end fraction adalah 0.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

S. Amamah

Mahasiswa/Alumni Universitas Negeri Malang

Terakhir diupdate 07 Juni 2021

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Pertanyaan yang serupa

28.

Pembahasan Soal:

Perhatikan penghitungan berikut!

 sin open parentheses 270 degree close parentheses equals sin open parentheses 180 degree plus 90 degree close parentheses equals negative sin space 90 degree equals negative 1 open parentheses kuadran space III close parentheses cos open parentheses 135 degree close parentheses equals cos open parentheses 180 degree minus 45 degree close parentheses equals negative cos space 45 degree equals negative 1 half square root of 2 space open parentheses kuadran space II close parentheses tan open parentheses 135 degree close parentheses equals tan open parentheses 180 degree minus 45 degree close parentheses equals negative tan space 45 degree equals negative 1 space open parentheses kuadran space II close parentheses sin open parentheses 150 degree close parentheses equals sin open parentheses 180 degree minus 30 degree close parentheses equals sin space 30 degree equals 1 half open parentheses kuadran space II close parentheses cos open parentheses 225 degree close parentheses equals cos open parentheses 180 degree plus 45 degree close parentheses equals cos open parentheses 45 degree close parentheses equals negative 1 half square root of 2 open parentheses kuadran space III close parentheses  fraction numerator sin space 270 degree times cos space 135 degree minus tan space 135 degree over denominator sin space 150 degree times cos space 225 degree end fraction equals fraction numerator open parentheses negative 1 close parentheses times open parentheses negative 1 half square root of 2 close parentheses minus open parentheses negative 1 close parentheses over denominator open parentheses 1 half close parentheses times open parentheses negative 1 half square root of 2 close parentheses end fraction equals fraction numerator begin display style fraction numerator square root of 2 over denominator 2 end fraction end style plus 1 over denominator negative begin display style 1 fourth end style square root of 2 end fraction equals open parentheses fraction numerator square root of 2 over denominator 2 end fraction plus 1 close parentheses cross times fraction numerator 1 over denominator negative 1 fourth square root of 2 end fraction equals open parentheses fraction numerator square root of 2 over denominator 2 end fraction plus 2 over 2 close parentheses cross times fraction numerator 1 over denominator negative 1 fourth square root of 2 end fraction equals open parentheses fraction numerator square root of 2 plus 2 over denominator 2 end fraction close parentheses cross times fraction numerator 1 over denominator negative 1 fourth square root of 2 end fraction equals fraction numerator square root of 2 plus 2 over denominator 2 cross times open parentheses negative 1 fourth square root of 2 close parentheses end fraction equals fraction numerator square root of 2 plus 2 over denominator negative begin display style 1 half end style square root of 2 end fraction equals negative fraction numerator square root of 2 plus 2 over denominator begin display style 1 half end style square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction equals fraction numerator negative open parentheses open parentheses square root of 2 cross times square root of 2 close parentheses plus 2 square root of 2 close parentheses over denominator begin display style 1 half end style open parentheses square root of 2 cross times square root of 2 close parentheses end fraction equals fraction numerator negative open parentheses 2 plus 2 square root of 2 close parentheses over denominator begin display style 1 half open parentheses 2 close parentheses end style end fraction equals fraction numerator negative open parentheses 2 plus 2 square root of 2 close parentheses over denominator begin display style 1 end style end fraction equals negative open parentheses 2 plus 2 square root of 2 close parentheses           

Jadi, fraction numerator sin space 270 degree times cos space 135 degree minus tan space 135 degree over denominator sin space 150 degree times cos space 225 degree end fraction equals negative open parentheses 2 plus 2 square root of 2 close parentheses. 

Oleh karena itu, tidak ada jawaban yang benar. space 

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

Pembahasan Soal:

Ingat:

begin mathsize 14px style sin space left parenthesis 180 degree minus A right parenthesis equals sin space A cos space left parenthesis 180 degree plus A right parenthesis equals negative cos space A cos space left parenthesis 360 degree minus A right parenthesis equals cos space A end style

Jadi

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 left parenthesis 180 degree minus 30 degree right parenthesis plus sin space left parenthesis 180 degree minus 60 degree right parenthesis over denominator cos space left parenthesis 180 degree plus 30 degree right parenthesis minus cos space left parenthesis 360 degree minus 60 degree right parenthesis 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 plus 1 half square root of 3 end style 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

Roboguru

Nilai dari  ...

Pembahasan Soal:

Ubahlah sudut ke dalam bentuk sudut istimewa pada trigonometri.

Gunakan perbandingan trigonometri sudut-sudut berelasi.

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space open parentheses 180 degree minus alpha close parentheses end cell equals cell sin 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

Sehingga pada sin space 120 degree dan cos space 225 degree berlaku:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 120 degree end cell equals cell sin space open parentheses 180 degree minus 60 degree close parentheses end cell row blank equals cell sin space 60 degree end cell row blank blank blank row cell cos space 225 degree end cell equals cell cos space open parentheses 180 degree plus 45 degree close parentheses end cell row blank equals cell negative cos space 45 degree end cell end table

Diperoleh perhitungannya yaitu:

tan open parentheses negative 45 degree close parentheses plus sin space 120 degree plus cos space 225 degree minus cos space 30 degree equals tan open parentheses negative 45 degree close parentheses plus sin space 60 degree plus open parentheses negative cos space 4 5 degree close parentheses minus cos space 30 degree equals negative 1 plus 1 half square root of 3 plus open parentheses negative 1 half square root of 2 close parentheses minus 1 half square root of 3 equals negative 1 plus down diagonal strike 1 half square root of 3 end strike minus 1 half square root of 2 minus down diagonal strike 1 half square root of 3 end strike equals negative 1 minus 1 half square root of 2

Nilai dari tan open parentheses negative 45 degree close parentheses plus sin space 120 degree plus cos space 225 degree minus cos space 30 degree equalsnegative 1 minus 1 half square root of 2.

Roboguru

Tentukan hasil dari

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 5 sin left parenthesis 125 degree plus x right parenthesis plus 4 cos left parenthesis 145 degree minus x right parenthesis over denominator 4 sin left parenthesis 305 degree plus x right parenthesis minus 6 cos left parenthesis 215 degree plus x right parenthesis end fraction end cell equals cell fraction numerator 5 sin left parenthesis 90 degree plus 35 degree plus x right parenthesis plus 4 cos left parenthesis 180 degree minus 35 degree minus x right parenthesis over denominator 4 sin left parenthesis 270 degree plus 35 degree plus x right parenthesis minus 6 cos left parenthesis 180 degree plus 35 degree plus x right parenthesis end fraction end cell row blank equals cell fraction numerator 5 sin left parenthesis 90 degree plus left parenthesis 35 degree plus x right parenthesis right parenthesis plus 4 cos left parenthesis 180 degree minus left parenthesis 35 degree plus x right parenthesis right parenthesis over denominator 4 sin left parenthesis 270 degree plus left parenthesis 35 degree plus x right parenthesis right parenthesis minus 6 cos left parenthesis 180 degree plus left parenthesis 35 degree plus x right parenthesis right parenthesis end fraction end cell row blank equals cell fraction numerator 5 cos left parenthesis 35 degree plus x right parenthesis minus 4 cos left parenthesis 35 degree plus x right parenthesis over denominator negative 4 cos left parenthesis 35 degree plus x right parenthesis plus 6 cos left parenthesis 35 degree plus x right parenthesis end fraction end cell row blank equals cell fraction numerator cos left parenthesis 35 degree plus x right parenthesis over denominator 2 cos left parenthesis 35 degree plus x right parenthesis end fraction end cell row blank equals cell 1 half end cell end table end style 

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