Pertanyaan

Nilai dari ekspresi cos − 1 ( 2 1 ) − cos − 1 ( 2 2 ) + cos − 1 ( 2 3 ) adalah ....

Nilai dari ekspresi

$cos^{- 1} (\frac{1}{2}) - cos^{- 1} (\frac{2}{2}) + cos^{- 1} (\frac{3}{2})$

adalah ....

Y. Umi

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Ingat! Jika , maka . Konversi sudut ke radian Diketahui . Untuk Dengan demikian, Jadi, . Jadi, jawaban yang tepat adalah A.

Ingat!

Jika cos to the power of negative 1 end exponent y equals x , maka cos space x equals y .

Konversi sudut ke radian

a degree equals a middle dot pi over 180 space radian

Diketahui $cos to the power of negative sign 1 end exponent open parentheses 1 half close parentheses minus sign cos to the power of negative sign 1 end exponent open parentheses fraction numerator square root of 2 over denominator 2 end fraction close parentheses plus cos to the power of negative sign 1 end exponent open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses$ . Untuk

table attributes columnalign right center left columnspacing 0px end attributes row cell cos to the power of negative sign 1 end exponent open parentheses 1 half close parentheses end cell equals italic x row cell cos space italic x end cell equals cell 1 half end cell row italic x equals cell 60 degree end cell end table

$table attributes columnalign right center left columnspacing 0px end attributes row cell cos to the power of negative sign 1 end exponent open parentheses fraction numerator square root of 2 over denominator 2 end fraction close parentheses end cell equals italic x row cell cos space italic x end cell equals cell fraction numerator square root of 2 over denominator 2 end fraction end cell row italic x equals cell 45 degree end cell end table$

$table attributes columnalign right center left columnspacing 0px end attributes row cell cos to the power of negative sign 1 end exponent open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses end cell equals italic x row cell cos space italic x end cell equals cell fraction numerator square root of 3 over denominator 2 end fraction end cell row italic x equals cell 30 degree end cell end table$

Dengan demikian,

$table attributes columnalign right center left columnspacing 0px end attributes row cell cos to the power of negative sign 1 end exponent open parentheses 1 half close parentheses minus sign cos to the power of negative sign 1 end exponent open parentheses fraction numerator square root of 2 over denominator 2 end fraction close parentheses plus cos to the power of negative sign 1 end exponent open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses end cell equals cell 60 degree minus sign 45 degree plus 30 degree end cell row blank equals cell 45 degree end cell row blank equals cell 45 middle dot pi over 180 end cell row blank equals cell pi over 2 end cell end table$

Jadi, $table attributes columnalign right center left columnspacing 0px end attributes row cell cos to the power of negative sign 1 end exponent open parentheses 1 half close parentheses minus sign cos to the power of negative sign 1 end exponent open parentheses fraction numerator square root of 2 over denominator 2 end fraction close parentheses plus cos to the power of negative sign 1 end exponent open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses end cell equals cell pi over 2 end cell end table$ .

Jadi, jawaban yang tepat adalah A.