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Tentukan nilai

Pertanyaan

Tentukan nilai sin space 45 degree cross times cos space 45 degree plus tan space 30 degree cross times tan space 60 degree

Pembahasan Soal:

Ingat nilai dari sudut-sudut istimewa yaitu 30 degree45 degree60 degree baik Sin, Cos, maupunspace Tan

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 45 degree cross times cos space 45 degree plus tan space 30 degree cross times tan space 60 degree end cell equals cell 1 half square root of 2 cross times 1 half square root of 2 plus 1 third square root of 3 cross times square root of 3 end cell row blank equals cell 1 fourth cross times 2 plus 1 third cross times 3 end cell row blank equals cell 1 half plus 1 end cell row blank equals cell 1 half plus 2 over 2 end cell row blank equals cell 3 over 2 end cell end table

Jadi, dapat disimpulkan bahwa nilai dari sin space 45 degree cross times cos space 45 degree plus tan space 30 degree cross times tan space 60 degree adalah 3 over 2.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

M. Iqbal

Mahasiswa/Alumni Universitas Negeri Semarang

Terakhir diupdate 05 Juni 2021

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Pertanyaan yang serupa

Nilai dari  dikurangi dengan  adalah ....

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator sin open parentheses 30 degree close parentheses plus cos open parentheses 60 degree close parentheses over denominator tan open parentheses 45 degree close parentheses end fraction minus fraction numerator sin squared open parentheses 45 degree close parentheses over denominator tan squared open parentheses 45 degree close parentheses 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 over denominator 1 end fraction minus fraction numerator begin display style 1 half end style over denominator begin display style 1 half end style end fraction end cell row blank equals cell 1 minus 1 end cell row blank equals 0 end table end style

Jadi, Jawaban yang tepat adalah A.

0

Roboguru

Nilai dari

Pembahasan Soal:

Ingat!

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

Maka,

 table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell sin space 45 degree plus cos space 135 degree minus open parentheses tan space 60 degree close parentheses squared end cell row blank equals cell sin space 45 degree plus cos space open parentheses 180 degree minus 45 degree close parentheses minus open parentheses tan space 60 degree close parentheses squared end cell row blank equals cell sin space 45 degree minus cos space 45 degree minus open parentheses tan space 60 degree close parentheses squared end cell row blank equals cell 1 half square root of 2 minus 1 half square root of 2 minus open parentheses square root of 3 close parentheses squared end cell row blank equals cell negative 3 end cell end table 

Jadi, Error converting from MathML to accessible text..

0

Roboguru

Hitung nilai dari: b.

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.

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Roboguru

Pembahasan Soal:

Hasil dari fraction numerator sin space 60 degree plus tan space 45 degree plus cos space 30 degree over denominator cosec space 60 degree space cotan space 45 degree end fraction:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sin space 60 degree plus tan space 45 degree plus cos space 30 degree over denominator cosec space 60 degree space cotan space 45 degree end fraction end cell equals cell fraction numerator sin space 60 degree plus tan space 45 degree plus cos space 30 degree over denominator begin display style fraction numerator 1 over denominator sin space 60 degree end fraction end style cross times begin display style fraction numerator 1 over denominator tan space 45 degree end fraction end style space end fraction end cell row blank equals cell fraction numerator begin display style 1 half end style square root of 3 plus 1 plus begin display style 1 half end style square root of 3 over denominator begin display style fraction numerator 1 over denominator begin display style 1 half end style square root of 3 end fraction end style cross times begin display style 1 over 1 end style end fraction end cell row blank equals cell fraction numerator 1 plus square root of 3 over denominator begin display style fraction numerator 2 over denominator square root of 3 end fraction end style end fraction end cell row blank equals cell fraction numerator open parentheses 1 plus square root of 3 close parentheses square root of 3 over denominator 2 end fraction end cell row blank equals cell fraction numerator square root of 3 plus 3 over denominator 2 end fraction end cell end table 

Jadi, hasil dari fraction numerator sin space 60 degree plus tan space 45 degree plus cos space 30 degree over denominator cosec space 60 degree space cotan space 45 degree end fraction adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 3 plus 3 over denominator 2 end fraction end cell end table.

0

Roboguru

Hitunglah .

Pembahasan Soal:

Dalam trigonometri, terdapat sudut-sudut istimewa yang nilainya sudah ada. Berikut adalah tabel nilai sudut istimewa:

Berdasarkan tabel di atas, maka

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space 60 degree plus tan space 45 degree end cell equals cell 1 half plus 1 end cell row blank equals cell 3 over 2. end cell end table  

Dengan demikian, nilai dari cos space 60 degree plus tan space 45 degree adalah 3 over 2.

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