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Hitung nilai dari: b. cos150∘+sin45∘+21​cot(−330∘)

Pertanyaan

Hitung nilai dari:

b. begin mathsize 14px style cos space 150 degree plus sin space 45 degree plus 1 half cot open parentheses negative 330 degree close parentheses end style  

Pembahasan Soal:

Nilai cos pada kuadran II adalah negatif sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space 150 degree end cell equals cell cos space open parentheses 180 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 end table 

Kemudian gunakna definisi cotangen dan konsep sudut negatif, ingat nilai tangen pada kuadran IV adalah negatif sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell cot space open parentheses negative 330 degree close parentheses end cell equals cell fraction numerator 1 over denominator tan space open parentheses negative 330 degree close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator negative tan space 330 degree end fraction end cell row blank equals cell fraction numerator 1 over denominator negative tan space open parentheses 360 degree minus 30 degree close parentheses end fraction end cell row blank equals cell negative fraction numerator 1 over denominator negative tan space 30 degree end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style fraction numerator square root of 3 over denominator 2 end fraction end style end fraction end cell row blank equals cell fraction numerator 2 over denominator square root of 3 end fraction end cell row blank equals cell fraction numerator 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 2 over 3 square root of 3 end cell end table  

Kemudian substitusikan:

cos space 150 degree plus sin space 45 degree plus 1 half cot space open parentheses negative 330 degree close parentheses equals negative 1 half square root of 3 plus 1 half square root of 2 plus 1 half open parentheses 2 over 3 square root of 3 close parentheses equals negative 1 half square root of 3 plus 1 half square root of 2 plus 1 third square root of 3 equals 1 half square root of 2 plus 1 third square root of 3 minus 1 half square root of 3 equals 1 half square root of 2 minus 1 over 6 square root of 3  

Dengan demikian nilai dari begin mathsize 14px style cos space 150 degree plus sin space 45 degree plus 1 half cot open parentheses negative 330 degree close parentheses end style adalah 1 half square root of 2 minus 1 over 6 square root of 3.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

S. Amamah

Mahasiswa/Alumni Universitas Negeri Malang

Terakhir diupdate 06 Oktober 2021

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Pertanyaan yang serupa

Tentukan nilai dari trigonometri berikut: e. cot(−47​π)

Pembahasan Soal:

Gunakan konsep sudut negatif dan definisi cotangen, ingat pada kuadran III tangen bernilai negatif sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell cot space open parentheses negative 7 over 4 straight pi close parentheses end cell equals cell cot space open parentheses negative 7 over 4 cross times 180 degree close parentheses end cell row blank equals cell cot space open parentheses negative 315 degree close parentheses end cell row blank equals cell fraction numerator 1 over denominator tan space open parentheses negative 315 degree close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator negative tan space 315 degree end fraction end cell row blank equals cell fraction numerator 1 over denominator negative tan space open parentheses 360 degree minus 45 degree close parentheses space end fraction end cell row blank equals cell fraction numerator 1 over denominator negative open parentheses negative tan space 45 degree close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator negative open parentheses negative 1 close parentheses end fraction end cell row blank equals 1 end table 

Dengan demikian nilai begin mathsize 14px style cot space open parentheses negative 7 over 4 straight pi close parentheses end style adalah 1.

0

Roboguru

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 cos2225∘tan2225∘+cos240∘+sin330∘​ adalah ...

Pembahasan Soal:

Ingat konsep nilai sudut pada kuadran III dan IV sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space 225 degree end cell equals cell tan space open parentheses 180 degree plus 45 degree close parentheses end cell row blank equals cell tan space 45 degree end cell row blank equals 1 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 row cell sin space 330 degree end cell equals cell sin space open parentheses 360 degree minus 30 degree close parentheses end cell row blank equals cell negative sin space 30 degree end cell row blank equals cell negative 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:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator tan squared space 225 degree plus cos space 240 degree plus sin space 330 degree over denominator cos squared space 225 degree end fraction end cell equals cell fraction numerator open parentheses 1 close parentheses squared plus open parentheses negative begin display style 1 half end style close parentheses plus open parentheses negative 1 half close parentheses over denominator open parentheses negative begin display style 1 half end style square root of 2 close parentheses squared end fraction end cell row blank equals cell fraction numerator 1 minus 1 over denominator begin display style 1 fourth end style times 2 end fraction end cell row blank equals 0 end table 

Oleh karena itu, jawaban yang benar adalah D.

0

Roboguru

cos(330∘)⋅tan(−135∘)−sin(−210∘)⋅cotan330∘=....

Pembahasan Soal:

Untuk menyelesaikan soal, ubahlah sudut-sudut menjadi sudut pada kuadran I.

cos(330)tan(135)sin(210)cotan330=cos30tan45sin30tan301=(231)21331=23(21(33))=23(23333)=23+633=633+33=663=3   

Dengan demikian, begin mathsize 11px style cos left parenthesis 330 degree right parenthesis times tan left parenthesis negative 135 degree right parenthesis minus space sin left parenthesis negative 210 degree right parenthesis times cotan space 330 degree equals square root of 3 end style .

0

Roboguru

Tentukan nilai dari trigonometri berikut: d. sec(−135∘)

Pembahasan Soal:

Gunakan konsep sudut negatif dan definisi secan, ingat nilai cos pada kuadran II adalah negatif sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell sec space open parentheses negative 135 degree close parentheses end cell equals cell fraction numerator 1 over denominator cos space open parentheses negative 135 degree close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator cos space 135 degree end fraction end cell row blank equals cell fraction numerator 1 over denominator cos open parentheses 180 degree minus 45 degree close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator negative cos space 45 degree end fraction end cell row blank equals cell negative fraction numerator 1 over denominator begin display style fraction numerator square root of 2 over denominator 2 end fraction end style end fraction end cell row blank equals cell negative 1 cross times fraction numerator 2 over denominator square root of 2 end fraction end cell row blank equals cell 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 end cell row blank equals cell negative 2 over 2 square root of 2 end cell row blank equals cell negative square root of 2 end cell end table

Dengan demikian nilai begin mathsize 14px style sec space open parentheses negative 135 degree close parentheses end style adalah negative square root of 2 .

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