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Himpunan semua bilangan real x pada selang  yang m...

Himpunan semua bilangan real x pada selang open square brackets straight pi comma 2 straight pi close square brackets yang memenuhi sin left parenthesis 2 x right parenthesis minus 2 cos squared x greater or equal than negative 2 berbentuk [a,b]. Nilai a+b adalah...

  1. fraction numerator 9 straight pi over denominator 4 end fraction

  2. fraction numerator 10 straight pi over denominator 4 end fraction

  3. fraction numerator 11 straight pi over denominator 4 end fraction

  4. fraction numerator 13 straight pi over denominator 4 end fraction

  5. fraction numerator 14 straight pi over denominator 4 end fraction

Jawaban:

sin invisible function application left parenthesis 2 straight x right parenthesis minus 2 cos squared invisible function application straight x greater or equal than negative 2  sin invisible function application left parenthesis 2 straight x right parenthesis plus 2 minus 2 cos squared invisible function application straight x greater or equal than 0  sin invisible function application left parenthesis 2 straight x right parenthesis plus 2 left parenthesis 1 minus cos squared invisible function application straight x right parenthesis greater or equal than 0  sin invisible function application left parenthesis 2 straight x right parenthesis plus 2 sin squared invisible function application straight x greater or equal than 0  2 sin invisible function application xcos invisible function application straight x plus 2 sin squared invisible function application straight x greater or equal than 0  sin invisible function application xcos invisible function application straight x plus sin squared invisible function application straight x greater or equal than 0  sin invisible function application straight x left parenthesis cos invisible function application straight x plus sin invisible function application straight x right parenthesis greater or equal than 0    Didapat space pembuat space nol comma space yaitu  box enclose sin space straight x equals 0 end enclose space atau space box enclose sin space straight x equals negative cos space straight x end enclose    Untuk space sin invisible function application straight x equals 0 rightwards double arrow box enclose straight x equals straight pi comma 2 straight pi end enclose  Untuk space sinx equals negative cos rightwards double arrow tan space straight x equals negative 1 rightwards double arrow box enclose straight x equals 7 over 4 straight pi end enclose

Sehingga space didapat space daerah space penyelesaian  box enclose straight pi less or equal than straight x less or equal than 7 over 4 straight pi end enclose  Maka  box enclose straight a equals straight pi end enclose  box enclose straight b equals 7 over 4 straight pi end enclose  Sehingga  straight a plus straight b equals straight pi plus 7 over 4 straight pi equals box enclose 11 over 4 straight pi end enclose

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