Pertanyaan

Nilai dari ekspresi cos − 1 ( 0 ) − cos − 1 ( 2 1 ) + cos − 1 ( 2 2 ) − cos − 1 ( 2 3 ) adalah ....

Nilai dari ekspresi

$cos^{- 1} (0) - cos^{- 1} (\frac{1}{2}) + cos^{- 1} (\frac{2}{2}) - cos^{- 1} (\frac{3}{2})$

adalah ....

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Klaim

Y. Umi

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Ingat! Jika , maka . Diketahui . Untuk Dengan demikian, Jadi, . Jadi, jawaban yang tepat adalah E.

Ingat!

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

Diketahui $cos to the power of negative sign 1 end exponent open parentheses 0 close parentheses minus sign cos to the power of negative sign 1 end exponent open parentheses 1 half close parentheses plus cos to the power of negative sign 1 end exponent open parentheses fraction numerator square root of 2 over denominator 2 end fraction close parentheses minus sign cos to the power of negative sign 1 end exponent open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses$ . Untuk

cos to the power of negative sign 1 end exponent open parentheses 0 close parentheses equals 90 degree

cos to the power of negative sign 1 end exponent open parentheses 1 half close parentheses equals 60 degree

$cos to the power of negative sign 1 end exponent open parentheses fraction numerator square root of 2 over denominator 2 end fraction close parentheses equals 45 degree$

$cos to the power of negative sign 1 end exponent open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses equals 30 degree$

Dengan demikian,

$table attributes columnalign right center left columnspacing 0px end attributes row cell cos to the power of negative sign 1 end exponent open parentheses 0 close parentheses minus sign cos to the power of negative sign 1 end exponent open parentheses 1 half close parentheses plus cos to the power of negative sign 1 end exponent open parentheses fraction numerator square root of 2 over denominator 2 end fraction close parentheses minus sign cos to the power of negative sign 1 end exponent open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses end cell equals cell 90 degree minus sign 60 degree plus 45 degree minus sign 30 degree end cell row blank equals cell 45 degree end cell end table$

Jadi, $cos to the power of negative sign 1 end exponent open parentheses 0 close parentheses minus sign cos to the power of negative sign 1 end exponent open parentheses 1 half close parentheses plus cos to the power of negative sign 1 end exponent open parentheses fraction numerator square root of 2 over denominator 2 end fraction close parentheses minus sign cos to the power of negative sign 1 end exponent open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses equals 45 degree$ .

Jadi, jawaban yang tepat adalah E.