Pertanyaan

Diketahui cos 2 A − sin 2 A = 25 24 . Untuk A sudut lancip nilai sin A sama dengan ...

Diketahui $cos^{2} A - sin^{2} A = \frac{24}{25}$ . Untuk $A$ sudut lancip nilai $sin A$ sama dengan ... $\;$

$fraction numerator square root of 2 over denominator 10 end fraction$
$fraction numerator square root of 3 over denominator 10 end fraction$
$fraction numerator square root of 5 over denominator 10 end fraction$
$fraction numerator square root of 7 over denominator 10 end fraction$

Ikuti Tryout SNBT & Menangkan E-Wallet 100rb

Habis dalam

Klaim

A. Armanda

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Sudut Rangkap pada Cosinus Diketahui dan sudut lancip (terletak dikuadran I), maka bernilai positif. Sehingga, . Jadi, jawaban yang tepat adalah B.

Sudut Rangkap pada Cosinus

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space 2 alpha end cell equals cell cos squared space alpha minus sin squared space alpha end cell row blank equals cell 2 space cos squared space alpha minus 1 end cell row blank equals cell 1 minus 2 space sin squared space alpha end cell end table

Diketahui cos squared space straight A minus sin squared space straight A equals 24 over 25 dan sudut lancip (terletak dikuadran I), maka sin space straight A bernilai positif.

$table attributes columnalign right center left columnspacing 0px end attributes row cell cos squared space straight A minus sin squared space straight A end cell equals cell 24 over 25 end cell row cell cos space 2 straight A end cell equals cell 24 over 25 end cell row cell 1 minus 2 space sin squared space straight A end cell equals cell 24 over 25 end cell row cell 1 minus 24 over 25 end cell equals cell 2 space sin squared space straight A end cell row cell 25 over 25 minus 24 over 25 end cell equals cell 2 space sin squared space straight A end cell row cell 1 over 25 end cell equals cell 2 space sin squared space straight A end cell row cell fraction numerator 1 over denominator 25 times 2 end fraction end cell equals cell sin squared space straight A end cell row cell sin squared space straight A end cell equals cell fraction numerator 1 over denominator 25 times 2 end fraction end cell row cell sin space straight A end cell equals cell plus-or-minus square root of fraction numerator 1 over denominator 25 times 2 end fraction end root end cell row cell sin space straight A end cell equals cell square root of fraction numerator 1 over denominator 25 times 2 end fraction end root space open parentheses sin space straight A space bernilai space positif close parentheses end cell row cell sin space straight A end cell equals cell fraction numerator 1 over denominator 5 square root of 2 end fraction cross times fraction numerator 5 square root of 2 over denominator 5 square root of 2 end fraction end cell row cell sin space straight A end cell equals cell fraction numerator up diagonal strike 5 square root of 2 over denominator up diagonal strike 50 end fraction end cell row cell sin space straight A end cell equals cell fraction numerator square root of 2 over denominator 10 end fraction end cell end table$

Sehingga, $table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight A end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 2 over denominator 10 end fraction end cell end table$ .

Jadi, jawaban yang tepat adalah B.