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Himpunan penyelesaian persamaan untuk adalah ....

Himpunan penyelesaian persamaan square root of 6 space sin space x to the power of o space plus space square root of 2 space cos space x to the power of o space equals space 2 comma untuk 0 less or equal than x less than 360 adalah ....

  1. {15, 105}

  2. {15,195}

  3. {75, 195}

  4. {75, 345}

  5. {105, 345}

Jawaban:

square root of 6 space sin space x to the power of o space plus space square root of 2 space cos space x to the power of o space equals space 2 space rightwards arrow space k space cos left parenthesis x minus alpha right parenthesis  k equals square root of left parenthesis square root of 2 right parenthesis squared plus left parenthesis square root of 6 end root right parenthesis squared equals square root of 8 equals 2 square root of 2  tan space alpha equals fraction numerator square root of 6 over denominator square root of 2 end fraction equals fraction numerator square root of 3 cross times square root of 2 over denominator square root of 2 end fraction equals square root of 3  alpha equals 60 to the power of 0

Maka :

k space cos space left parenthesis x minus alpha right parenthesis equals 2  2 square root of 2 space cos space left parenthesis x minus 60 to the power of 0 right parenthesis equals 2  cos left parenthesis x minus 60 to the power of 0 right parenthesis equals 1 half square root of 2

Jadi,

x minus 60 to the power of 0 equals 45  x equals 105    x minus 60 to the power of 0 equals negative 45  x equals 15

0

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