Pertanyaan

Nilai dari ekspresi: sin ( cos − 1 ( − 3 1 ) ) × tan ( sin − 1 ( 29 20 ) ) adalah ....

Nilai dari ekspresi:

$sin (cos^{- 1} (- \frac{1}{3})) \times tan (sin^{- 1} (\frac{20}{29}))$

adalah ....

S. Difhayanti

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. Dr. Hamka

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Ingat kembali rumus invers fungsi trigonometri berikut. Sehingga, diperoleh berikut ini. Dengan demikian, nilai dari ekspresi adalah . Oleh karena itu, jawaban yang benar adalah A.

Ingat kembali rumus invers fungsi trigonometri berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell sin space open parentheses cos to the power of negative 1 end exponent open parentheses x close parentheses close parentheses end cell equals cell square root of 1 minus x squared end root end cell row cell tan space open parentheses sin to the power of negative 1 end exponent open parentheses x close parentheses close parentheses end cell equals cell fraction numerator x square root of 1 minus x squared end root over denominator 1 minus x squared end fraction end cell end table$

Sehingga, diperoleh berikut ini.

$table attributes columnalign right center left columnspacing 0px end attributes row cell sin space open parentheses cos to the power of negative 1 end exponent open parentheses negative 1 third close parentheses close parentheses end cell equals cell square root of 1 minus x squared end root end cell row blank equals cell square root of 1 minus open parentheses negative 1 third close parentheses squared end root end cell row blank equals cell square root of 1 minus 1 over 9 end root end cell row blank equals cell square root of 8 over 9 end root end cell row blank equals cell 1 third square root of 8 end cell row blank equals cell fraction numerator 2 square root of 2 over denominator 3 end fraction end cell end table$

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan space open parentheses sin to the power of negative 1 end exponent open parentheses 20 over 29 close parentheses close parentheses end cell equals cell fraction numerator begin display style 20 over 29 end style square root of 1 minus open parentheses begin display style 20 over 29 end style close parentheses squared end root over denominator 1 minus open parentheses begin display style 20 over 29 end style close parentheses squared end fraction end cell row blank equals cell fraction numerator begin display style 20 over 29 end style square root of 1 minus begin display style 400 over 841 end style end root over denominator 1 minus begin display style 400 over 841 end style end fraction end cell row blank equals cell fraction numerator begin display style 20 over 29 square root of 441 over 841 end root end style over denominator begin display style 441 over 841 end style end fraction end cell row blank equals cell fraction numerator begin display style 20 over 29 times bevelled fraction numerator 21 over denominator square root of 841 end fraction end style over denominator begin display style 441 over 841 end style end fraction end cell row blank equals cell fraction numerator begin display style 20 over 29 times 21 over 29 end style over denominator begin display style 441 over 841 end style end fraction end cell row blank equals cell fraction numerator begin display style 420 over 841 end style over denominator begin display style 441 over 841 end style end fraction end cell row blank equals cell fraction numerator 420 over denominator up diagonal strike 841 end fraction cross times fraction numerator up diagonal strike 841 over denominator 441 end fraction end cell row blank equals cell fraction numerator 420 divided by 21 over denominator 441 divided by 21 end fraction end cell row blank equals cell 20 over 21 end cell end table$

$fraction numerator 2 square root of 2 over denominator 3 end fraction cross times 20 over 21 equals 40 over 63 square root of 2$

Dengan demikian, nilai dari ekspresi adalah 40 over 63 square root of 2 .

Oleh karena itu, jawaban yang benar adalah A.