Pertanyaan

Hitunglah tanpa menggunakankalkulator atau tabel trigonometri. d. cos ec [ sin − 1 ( 2 1 ) − cos − 1 ( 2 1 ) ]

Hitunglah tanpa menggunakan kalkulator atau tabel trigonometri.

d. $cos ec [sin^{- 1} (\frac{1}{2}) - cos^{- 1} (\frac{1}{2})]$

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Habis dalam

Klaim

Y. Umi

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

tidak ada solusi untuk .

tidak ada solusi untuk cos e c open square brackets sin to the power of negative 1 end exponent open parentheses 1 half close parentheses minus cos to the power of negative 1 end exponent open parentheses 1 half close parentheses close square brackets

cos e c open square brackets sin to the power of negative 1 end exponent open parentheses 1 half close parentheses minus cos to the power of negative 1 end exponent open parentheses 1 half close parentheses close square brackets

Pembahasan

Ingat! Jika , maka Jika , maka Diketahui . Jika , maka . Dengan pythagoras diperoleh Jika , maka . Dengan pythagoras diperoleh Kemudian, Jadi, tidak ada solusi untuk .

Ingat!

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

Jika sin to the power of negative sign 1 end exponent italic y equals italic x , maka y equals sin space x

Diketahui cos e c open square brackets sin to the power of negative 1 end exponent open parentheses 1 half close parentheses minus cos to the power of negative 1 end exponent open parentheses 1 half close parentheses close square brackets .

Jika , maka . Dengan pythagoras diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space x end cell equals cell depan over miring end cell row blank equals cell 1 half end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row samping equals cell square root of miring squared minus sign depan squared end root end cell row blank equals cell square root of 2 squared minus sign 1 squared end root end cell row blank equals cell square root of 4 minus sign 1 end root end cell row blank equals cell square root of 3 end cell end table

$table attributes columnalign right center left columnspacing 0px end attributes row cell cos space x end cell equals cell samping over miring end cell row blank equals cell fraction numerator square root of 3 over denominator 2 end fraction end cell end table$

Jika , maka . Dengan pythagoras diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space y end cell equals cell samping over miring end cell row blank equals cell 1 half end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row depan equals cell square root of miring squared minus sign samping squared end root end cell row blank equals cell square root of 2 squared minus sign 1 squared end root end cell row blank equals cell square root of 4 minus sign 1 end root end cell row blank equals cell square root of 3 end cell end table

$table attributes columnalign right center left columnspacing 0px end attributes row cell sin space y end cell equals cell depan over miring end cell row blank equals cell fraction numerator square root of 3 over denominator 2 end fraction end cell end table$

Kemudian,

$table attributes columnalign right center left columnspacing 0px end attributes row cell cos e c open parentheses x minus y close parentheses end cell equals cell fraction numerator 1 over denominator sin open parentheses x minus y close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator sin space x times cos space y minus sin space y times cos space x end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style 1 half end style times begin display style fraction numerator square root of 3 over denominator 2 end fraction end style minus begin display style fraction numerator square root of 3 over denominator 2 end fraction end style times begin display style 1 half end style end fraction end cell row blank equals cell fraction numerator 1 over denominator fraction numerator square root of 3 over denominator 4 end fraction minus fraction numerator square root of 3 over denominator 4 end fraction end fraction end cell row blank equals cell 1 over 0 end cell row blank equals cell tidak space terdefinisi end cell end table$

Jadi, tidak ada solusi untuk cos e c open square brackets sin to the power of negative 1 end exponent open parentheses 1 half close parentheses minus cos to the power of negative 1 end exponent open parentheses 1 half close parentheses close square brackets .