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Apabila  sudut lancip dan , maka nilai dari  adala...

Apabila theta sudut lancip dan cos space theta equals 3 over 5, maka nilai dari open parentheses fraction numerator sin space theta times tan space theta minus 1 over denominator 2 space tan squared space theta space end fraction close parentheses adalah ...

  1. 16 over 625 

  2. 1 over 36 

  3. 3 over 160 

  4. 160 over 3 

  5. 625 over 16 

Jawaban:

Diketahui cos space theta equals 3 over 5 dimana theta sudut lancip.

s a equals 3 m i equals 5

table attributes columnalign right center left columnspacing 0px end attributes row cell d e end cell equals cell square root of m i squared minus s a squared end root end cell row blank equals cell square root of 5 squared minus 3 squared end root end cell row blank equals cell square root of 25 minus 9 end root end cell row blank equals cell square root of 16 end cell row blank equals 4 end table 

Nilai open parentheses fraction numerator sin space theta times tan space theta minus 1 over denominator 2 space tan squared space theta space end fraction close parentheses:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator sin space theta times tan space theta minus 1 over denominator 2 space tan squared space theta space end fraction close parentheses end cell equals cell open parentheses fraction numerator begin display style fraction numerator d e over denominator m i end fraction end style times begin display style fraction numerator d e over denominator s a end fraction end style minus 1 over denominator 2 times open parentheses begin display style fraction numerator d e over denominator s a end fraction end style close parentheses squared end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator begin display style 4 over 5 end style times begin display style 4 over 3 end style minus 1 over denominator 2 times open parentheses begin display style 4 over 3 end style close parentheses squared end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator begin display style 16 over 15 end style minus 1 over denominator begin display style 32 over 9 end style end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator begin display style 1 over 15 end style over denominator begin display style 32 over 9 end style end fraction close parentheses end cell row blank equals cell 1 over 15 times 9 over 32 end cell row blank equals cell 3 over 160 end cell end table 

Sehingga, nilai dari open parentheses fraction numerator sin space theta times tan space theta minus 1 over denominator 2 space tan squared space theta space end fraction close parentheses adalah 3 over 160.

Jadi, jawaban yang tepat adalah C.

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