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Tentukan hasil dari sec 6 1 ​ π ⋅ tan 6 0 ∘ ⋅ sin 2 1 ​ π tan 3 0 ∘ ⋅ cos 0 ∘ . cot 6 1 ​ π + cos 3 0 ∘ . csc 3 1 ​ π ​ !

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W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

hasilnya adalah .

hasilnya adalah 1.

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Pembahasan

Ingat kembali: Maka: Jadi, hasilnya adalah .

Ingat kembali:

tan space 30 degree equals fraction numerator square root of 3 over denominator 3 end fraction cos space 0 degree equals 1 cot space 1 over 6 straight pi equals cot space open parentheses 1 over 6 cross times 180 degree close parentheses equals cot space 30 degree equals fraction numerator 1 over denominator tan space 30 degree end fraction equals fraction numerator 3 over denominator square root of 3 end fraction cos space 30 degree equals fraction numerator square root of 3 over denominator 2 end fraction sin space 60 degree equals fraction numerator square root of 3 over denominator 2 end fraction csc space 1 third straight pi equals csc space open parentheses 1 third cross times 180 degree close parentheses equals csc space 60 degree equals fraction numerator 1 over denominator sin space 60 degree end fraction equals fraction numerator 2 over denominator square root of 3 end fraction sec space 1 over 6 straight pi equals sec space open parentheses 1 over 6 cross times 180 degree close parentheses equals sec space 30 degree equals fraction numerator 1 over denominator cos space 30 degree end fraction equals fraction numerator 2 over denominator square root of 3 end fraction tan space 60 degree equals square root of 3 sin space 1 half straight pi equals sin space open parentheses 1 half cross times 180 degree close parentheses equals sin space 90 degree equals 1 

Maka:

fraction numerator tan space 30 degree times cos space 0 degree. c o t space begin display style 1 over 6 end style straight pi plus cos space 30 degree times space csc space begin display style 1 third end style straight pi over denominator s e c space begin display style 1 over 6 end style straight pi times space tan space 60 degree. space sin space begin display style 1 half end style straight pi end fraction equals fraction numerator begin display style fraction numerator square root of 3 over denominator 3 end fraction end style times 1 times begin display style fraction numerator 3 over denominator square root of 3 end fraction end style plus begin display style fraction numerator square root of 3 over denominator 2 end fraction end style times begin display style fraction numerator 2 over denominator square root of 3 end fraction end style over denominator begin display style fraction numerator 2 over denominator square root of 3 end fraction end style times square root of 3 times 1 end fraction equals fraction numerator 1 plus 1 over denominator 2 end fraction equals 2 over 2 equals 1  

Jadi, hasilnya adalah 1.

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