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

Himpunan semua bilangan real x pada selang open square brackets 0 comma 2 straight pi close square brackets yang memenuhi 2 minus 2 sin squared x less or equal than square root of 3 cos x berbentuk open square brackets a comma b close square brackets space union space open square brackets c comma d close square brackets. Nilai a + b + c + d adalah ....

  1. 3 straight pi

  2. 3 1 half straight pi

  3. 4 straight pi

  4. 4 1 half straight pi

  5. 5 straight pi

Jawaban:

 

2 minus 2 sin squared invisible function application straight x less or equal than square root of 3 cos invisible function application straight x  2 open parentheses 1 minus sin squared invisible function application straight x close parentheses less or equal than square root of 3 cos invisible function application straight x  2 cos squared invisible function application straight x less or equal than square root of 3 cos invisible function application straight x  2 cos squared invisible function application straight x minus square root of 3 cos invisible function application straight x less or equal than 0  cos invisible function application straight x open parentheses 2 cos invisible function application straight x minus square root of 3 close parentheses less or equal than 0    Didapat space pembuat space nol comma space yaitu  box enclose cos invisible function application straight x equals 0 end enclose space atau space box enclose cos invisible function application straight x equals fraction numerator square root of 3 over denominator 2 end fraction end enclose    Untuk space cos invisible function application straight x equals 0 rightwards double arrow box enclose straight x equals straight pi over 2 comma 3 over 2 straight pi end enclose  Untuk space cos invisible function application straight x equals fraction numerator square root of 3 over denominator 2 end fraction rightwards double arrow box enclose straight x equals straight pi over 6 comma 11 over 6 straight pi end enclose

 

Maka space didapat space straight pi over 6 less or equal than straight x less or equal than straight pi over 2 space atau space fraction numerator 3 straight pi over denominator 2 end fraction less or equal than straight x less or equal than fraction numerator 11 straight pi over denominator 6 end fraction  atau space dengan space penulisan space lain space yaitu space box enclose open square brackets straight pi over 6 comma straight pi over 2 close square brackets union open square brackets fraction numerator 3 straight pi over denominator 2 end fraction comma fraction numerator 11 straight pi over denominator 6 end fraction close square brackets end enclose.    Jadi space straight a plus straight b plus straight c plus straight d equals straight pi over 6 plus straight pi over 2 plus fraction numerator 3 straight pi over denominator 2 end fraction plus fraction numerator 11 straight pi over denominator 6 end fraction equals box enclose 4 straight pi end enclose

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