Pertanyaan

Tentukanekspresi aljabar masing-masing ekspresi berikut. c. sin ( 2 cos − 1 x )

Tentukan ekspresi aljabar masing-masing ekspresi berikut.

c. $sin (2 cos^{- 1} x)$

Y. Umi

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

ekspresi dari .

ekspresi dari table attributes columnalign right center left columnspacing 0px end attributes row cell sin open parentheses 2 space cos to the power of negative sign 1 end exponent italic x close parentheses end cell equals cell 2 square root of 1 minus sign italic x squared end root end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell sin open parentheses 2 space cos to the power of negative sign 1 end exponent italic x close parentheses end cell equals cell 2 square root of 1 minus sign italic x squared end root end cell end table

Pembahasan

Ingat! Jika , maka Akan dicari , oleh karena itu dimisalkan . Dengan demikian diperoleh Oleh karena itu, Jadi, ekspresi dari .

Ingat!

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

Akan dicari sin open parentheses 2 space cos to the power of negative sign 1 end exponent italic x close parentheses , oleh karena itu dimisalkan . Dengan demikian diperoleh

$table attributes columnalign right center left columnspacing 0px end attributes row cell cos space italic y end cell equals cell samping over miring end cell row blank equals cell x over 1 end cell row depan equals cell square root of miring squared minus sign samping squared end root end cell row blank equals cell square root of 1 squared minus sign x squared end root end cell row blank equals cell square root of 1 minus sign x squared end root end cell row cell sin space y end cell equals cell depan over miring end cell row blank equals cell fraction numerator square root of 1 minus sign x squared end root over denominator x end fraction end cell end table$

Oleh karena itu,

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

Jadi, ekspresi dari table attributes columnalign right center left columnspacing 0px end attributes row cell sin open parentheses 2 space cos to the power of negative sign 1 end exponent italic x close parentheses end cell equals cell 2 square root of 1 minus sign italic x squared end root end cell end table .