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

Pertanyaan

Apabila sin space theta equals 5 over 13 dan theta sudut lancip, maka nilai dari square root of open parentheses 1 plus tan space theta close parentheses open parentheses 1 minus tan space theta close parentheses end root adalah ...

  1. 13 over 5 

  2. 12 over 15 

  3. 13 over 12 

  4. fraction numerator square root of 119 over denominator 12 end fraction 

  5. fraction numerator square root of 119 over denominator square root of 12 end fraction 

Pembahasan Soal:

Diketahui  sin space theta equals 5 over 13 dan theta sudut lancip.

d e equals 5 m i equals 13

table attributes columnalign right center left columnspacing 0px end attributes row cell s a end cell equals cell square root of m i squared minus d e squared end root end cell row blank equals cell square root of 13 squared minus 5 squared end root end cell row blank equals cell square root of 169 minus 25 end root end cell row blank equals cell square root of 144 end cell row blank equals 12 end table

Nilai dari square root of open parentheses 1 plus tan space theta close parentheses open parentheses 1 minus tan space theta close parentheses end root:

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of open parentheses 1 plus tan space theta close parentheses open parentheses 1 minus tan space theta close parentheses end root end cell equals cell square root of open parentheses 1 plus fraction numerator d e over denominator s a end fraction close parentheses open parentheses 1 minus fraction numerator d e over denominator s a end fraction close parentheses end root end cell row blank equals cell square root of open parentheses 1 plus 5 over 12 close parentheses open parentheses 1 minus 5 over 12 close parentheses end root end cell row blank equals cell square root of open parentheses fraction numerator 12 plus 5 over denominator 12 end fraction close parentheses open parentheses fraction numerator 12 minus 5 over denominator 12 end fraction close parentheses end root end cell row blank equals cell square root of open parentheses 17 over 12 close parentheses open parentheses 7 over 12 close parentheses end root end cell row blank equals cell square root of 119 over 144 end root end cell row blank equals cell fraction numerator square root of 119 over denominator 12 end fraction end cell end table

Sehingga, nilai dari square root of open parentheses 1 plus tan space theta close parentheses open parentheses 1 minus tan space theta close parentheses end root adalah fraction numerator square root of 119 over denominator 12 end fraction.

Jadi, jawaban yang tepat adalah D.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 19 Mei 2021

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