Pertanyaan

Himpunan penyelesaian persamaan cos 2 x − 2 cos x = − 1 untuk 0 ≤ x ≤ 2 π adalah . . .

Himpunan penyelesaian persamaan $cos 2 x - 2 cos x = - 1$ untuk $0 \leq x \leq 2 π$ adalah . . .

$open curly brackets 0 comma straight pi over 2 comma fraction numerator 3 straight pi over denominator 2 end fraction close curly brackets$
$open curly brackets 0 comma straight pi over 2 comma straight pi comma fraction numerator 3 straight pi over denominator 2 end fraction close curly brackets$
$open curly brackets 0 comma straight pi over 2 comma fraction numerator 2 straight pi over denominator 3 end fraction comma 2 straight pi close curly brackets$
$open curly brackets 0 comma straight pi over 2 comma fraction numerator 3 straight pi over denominator 2 end fraction comma 2 straight pi close curly brackets$

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Pembahasan

Kasus 1 Nilai sama dengan 0, jika berada pada sudut Kasus 2 Nilai sama dengan 1, jika berada pada sudut

cos space 2 x minus 2 space cos space x equals negative 1 open parentheses 2 space cos squared space x minus 1 close parentheses minus 2 space cos space x plus 1 equals 0 2 space cos squared space x minus 2 space cos squared space x equals 0 2 space cos squared space x open parentheses cos space x minus 1 close parentheses equals 0

Kasus 1

Nilai sama dengan 0, jika berada pada sudut

$2 space cos space x equals 0 space left right double arrow space cos space x equals 0 space space space space cos space x equals cos space 90 to the power of degree space space space space space space space space space space space space space cos space x equals cos space 270 space space space space x equals 90 to the power of degree equals pi over 2 space space space space space space space space space space space space space space space space space space space space space space space space x equals 270 to the power of degree equals fraction numerator 3 pi over denominator 2 end fraction$

Kasus 2

Nilai sama dengan 1, jika berada pada sudut

$therefore H P equals open curly brackets 0 comma pi over 2 comma fraction numerator 3 pi over denominator 2 end fraction comma 2 pi close curly brackets$