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Pertanyaan

Jika tan space straight theta equals straight n dan 90 degree less than straight theta less than 180 degree, maka cos space straight theta times sin space straight theta equals.... 

  1. negative fraction numerator 1 over denominator 1 plus straight n squared end fraction 

  2. negative open parentheses 1 plus straight n squared close parentheses 

  3. fraction numerator negative straight n over denominator square root of 1 plus straight n squared end root end fraction 

  4. fraction numerator straight n over denominator square root of 1 plus straight n squared end root end fraction 

  5. negative square root of 1 plus straight n squared end root 

Pembahasan Soal:

Diketahui:

space space space space space space space space space space space space space tan space straight theta equals straight n fraction numerator sisi space depan over denominator sisi space samping end fraction equals straight n over 1 space space space space space space space space space space space space space space space de over sa equals straight n over 1   dan   90 degree less than straight theta less than 180 degree rightwards arrow Kuadran space II Kuadran space II rightwards arrow open parentheses sin space open parentheses plus close parentheses close parentheses 

Maka:

sisi space miring equals mi mi equals square root of de squared plus sa squared end root mi equals square root of straight n squared plus 1 squared end root mi equals square root of straight n squared plus 1 end root 

Sehingga:

cos space straight theta equals sa over mi equals fraction numerator 1 over denominator square root of straight n squared plus 1 end root end fraction rightwards arrow with kuadran space II on top space cos space straight theta equals negative fraction numerator 1 over denominator square root of straight n squared plus 1 end root end fraction sin space straight theta equals de over mi equals fraction numerator straight n over denominator square root of straight n squared plus 1 end root end fraction 

Berarti:

cos space straight theta times sin space straight theta equals negative fraction numerator 1 over denominator square root of straight n squared plus 1 end root end fraction times fraction numerator straight n over denominator square root of straight n squared plus 1 end root end fraction equals negative fraction numerator straight n over denominator straight n squared plus 1 end fraction 

Jadi, jawaban yang benar adalah negative fraction numerator straight n over denominator straight n squared plus 1 end fraction dan tidak ada pilihan jawaban yang tepat.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 26 April 2021

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