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Hitunglah nilai dari

Pertanyaan

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

Pembahasan Soal:

Iangtlah bahwa:

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

Diperoleh hasilnya yaitu:

fraction numerator sin space 270 degree times cos space 270 degree times tan space 270 degree over denominator sin space 150 degree times cos space 225 degree end fraction equals fraction numerator sin open parentheses 180 degree plus 90 degree close parentheses times cos open parentheses 180 degree plus 90 degree close parentheses times tan open parentheses 180 degree plus 90 degree close parentheses over denominator sin open parentheses 180 degree minus 30 degree close parentheses times cos open parentheses 180 degree plus 45 degree close parentheses end fraction equals fraction numerator negative sin space 90 degree times negative cos space 90 degree times tan space 90 degree over denominator sin space 30 degree times negative cos space 45 degree end fraction equals fraction numerator negative 1 times 0 times infinity 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 equals infinity

Maka, hasil dari fraction numerator sin space 270 degree times cos space 270 degree times tan space 270 degree over denominator sin space 150 degree times cos space 225 degree end fraction adalah infinity (Tak hingga).

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

S. Ayu

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Terakhir diupdate 04 Juni 2021

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Pertanyaan yang serupa

Hitunglah nilai dari

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.

0

Roboguru

Buktikan bahwa b.

Pembahasan Soal:

Dengan menggunakan hubungan sudut berelasi diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator cos open parentheses 180 plus p close parentheses times sec open parentheses 360 minus p close parentheses over denominator cotg open parentheses 180 minus p close parentheses times cotg open parentheses 90 minus p close parentheses end fraction end cell equals cell fraction numerator negative cos space p times sec space p over denominator negative cotg space p times tan space p end fraction end cell row blank equals cell fraction numerator cos space p times begin display style fraction numerator 1 over denominator cos space p end fraction end style over denominator begin display style fraction numerator 1 over denominator space tan space p end fraction end style times tan space p end fraction end cell row blank equals cell 1 over 1 end cell row blank equals 1 end table

Sehingga fraction numerator cos open parentheses 180 plus p close parentheses times sec open parentheses 360 minus p close parentheses over denominator cotg open parentheses 180 minus p close parentheses times cotg open parentheses 90 minus p close parentheses end fraction equals 1.

Dengan demikian tidak terbukti bahwa fraction numerator cos open parentheses 180 plus p close parentheses times sec open parentheses 360 minus p close parentheses over denominator cotg open parentheses 180 minus p close parentheses times cotg open parentheses 90 minus p close parentheses end fraction equals negative 1.

0

Roboguru

Nilai dari

Pembahasan Soal:

Ingat bahwa:

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

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

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

Sehingga diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 150 to the power of degree end cell equals cell sin space left parenthesis 180 minus 30 right parenthesis end cell row blank equals cell sin space 30 end cell row blank equals cell 1 half end cell row cell sin space 120 to the power of degree end cell equals cell sin space left parenthesis 180 minus 60 right parenthesis end cell row blank equals cell sin space 60 end cell row blank equals cell 1 half square root of 3 end cell row cell cos space 210 to the power of degree end cell equals cell cos space left parenthesis 180 plus 30 right parenthesis end cell row blank equals cell negative cos space 30 end cell row blank equals cell negative 1 half square root of 3 end cell row cell cos space 300 to the power of degree end cell equals cell cos space left parenthesis 360 minus 60 right parenthesis end cell row blank equals cell cos space 60 end cell row blank equals cell 1 half end cell end table 

Setelah mendapatkan hasilnya subsitusikan 

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sin space 150 to the power of degree plus sin space 120 to the power of degree over denominator cos space 210 to the power of degree minus cos space 300 to the power of degree end fraction end cell 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 end style left parenthesis 1 plus square root of 3 right parenthesis over denominator negative begin display style 1 half end style left parenthesis 1 plus square root of 3 right parenthesis end root end fraction end cell row blank equals cell negative 1 end cell end table

Oleh karena itu jawabannya adalah E

1

Roboguru

Nilai dari  ...

Pembahasan Soal:

Perbandingan trigonometri sudut berelasi merupakan perluasan dari definisi dasar trigonometri tentang kesebangunan pada segitiga siku-siku yang hanya memenuhi untuk sudut kuadran I atau sudut lancip begin mathsize 14px style left parenthesis 0 degree minus 90 degree right parenthesis end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator sin space 30 degree plus cos space 330 degree plus sin space 150 degree over denominator tan space 45 degree plus cos space 210 degree end fraction end cell row blank equals cell fraction numerator sin space 30 degree plus cos space left parenthesis 360 degree minus 30 degree right parenthesis plus sin space left parenthesis 180 degree minus 30 degree right parenthesis over denominator tan space 45 degree plus cos space left parenthesis 180 degree plus 30 degree right parenthesis end fraction end cell row blank equals cell fraction numerator sin space 30 degree plus cos space 30 degree plus sin space 30 degree over denominator tan space 45 degree minus cos 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 plus begin display style 1 half end style over denominator 1 minus begin display style 1 half end style square root of 3 end fraction end cell row blank equals cell fraction numerator 1 plus begin display style 1 half end style square root of 3 space space space space left enclose cross times 2 end enclose over denominator 1 minus begin display style 1 half end style square root of 3 space space space space left enclose cross times 2 end enclose end fraction end cell row blank equals cell fraction numerator 2 plus square root of 3 over denominator 2 minus square root of 3 end fraction end cell row blank blank blank row blank blank blank end table end style

Sehingga, nilai dari begin mathsize 14px style fraction numerator sin space 30 degree plus cos space 330 degree plus sin space 150 degree over denominator tan space 45 degree plus cos space 210 degree end fraction end style adalah begin mathsize 14px style fraction numerator 2 plus square root of 3 over denominator 2 minus square root of 3 end fraction end style.

Jadi, jawaban yang tepat adalah C.

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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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