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Pertanyaan

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

  1. straight pi

  2. 2 straight pi

  3. 3 straight pi

  4. 4 straight pi

  5. 5 straight pi

A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

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

Maka space didapat space 0 less or equal than straight x less or equal than straight pi over 3 space atau space fraction numerator 2 straight pi over denominator 3 end fraction less or equal than straight x less or equal than straight pi  atau space dengan space penulisan space lain space yaitu space box enclose open square brackets 0 comma straight pi over 3 close square brackets union open square brackets fraction numerator 2 straight pi over denominator 3 end fraction comma straight pi close square brackets end enclose.    Jadi space straight a plus straight b plus straight c plus straight d equals 0 plus straight pi over 3 plus fraction numerator 2 straight pi over denominator 3 end fraction plus straight pi equals box enclose 2 straight pi end enclose

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