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Himpunan semua bilangan real x pada selang [0,2π] yang memenuhi 2cos2x≤3−3cos2x berbentuk [a,b]∪[c,d]. Nilai a+b+c+d adalah.....

Pertanyaan

Himpunan semua bilangan real x pada selang left square bracket 0 comma 2 straight pi right square bracket yang memenuhi 2 cos squared x less or equal than 3 minus 3 cos 2 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

i right parenthesis S e d e r h a n a k a n space p e r t i d a k s a m a a n space y a n g space d i m i l i k i  2 cos squared invisible function application x less or equal than 3 minus 3 cos invisible function application 2 x  I n g a t space b a h w a space c o s invisible function application 2 x equals 2 c o s squared invisible function application x minus 1 comma space m a k a space p e r t i d a k s a m a a n space d i space a t a s space m e n j a d i  2 c o s squared invisible function application x less or equal than 3 minus 3 left parenthesis 2 c o s squared invisible function application x minus 1 right parenthesis  2 c o s squared invisible function application x less or equal than 3 minus 6 c o s squared invisible function application x plus 3  8 c o s squared invisible function application x minus 6 less or equal than 0  4 c o s squared invisible function application x minus 3 less or equal than 0  open parentheses 2 cos invisible function application x plus square root of 3 close parentheses open parentheses 2 cos invisible function application x minus square root of 3 close parentheses less or equal than 0    i i right parenthesis T e n t u k a n space p e m b u a t space n o l space p a d a space b e n t u k space d a r i space r u a s space k i r i space d a n space t e m p a t k a n space p a d a space g a r i s space b i l a n g a n  open parentheses 2 cos invisible function application x plus square root of 3 close parentheses open parentheses 2 cos invisible function application x minus square root of 3 close parentheses less or equal than 0  M a k a  2 cos invisible function application x plus square root of 3 equals 0  2 cos invisible function application x equals negative square root of 3  cos invisible function application x equals negative 1 half square root of 3    U n t u k space s e l a n g space left square bracket 0 comma 2 pi right square bracket space d i p e n u h i space u n t u k space x equals 5 over 6 pi space a t a u space x equals 7 over 6 pi  S e r t a  2 cos invisible function application x minus square root of 3 equals 0  2 cos invisible function application x equals square root of 3  cos invisible function application x equals 1 half square root of 3  U n t u k space s e l a n g space left square bracket 0 comma 2 pi right square bracket space d i p e n u h i space u n t u k space x equals 1 over 6 pi space a t a u space x equals 11 over 6 pi  P a d a space g a r i s space b i l a n g a n space colon

T a n d a space b u l a t space h i t a m space d i space a t a s space k a r e n a space p a d a space p e r t i d a k s a m a a n space d i space a t a s space m e n g a n d u n g space u n s u r space s a m a space d e n g a n space left parenthesis equals right parenthesis. space  K a r e n a space x space d i b a t a s i space p a d a space s e l a n g space left square bracket 0 comma 2 pi right square bracket comma space m a k a space g a r i s space b i l a n g a n space y a n g space d i b e n t u k space a d a l a h space d a r i space x equals 0 space h i n g g a space x equals 2 pi.    i i i right parenthesis T e n t u k a n space tan d a space d a r i space m a sin g minus m a sin g space d a e r a h. space  K a r e n a space n i l a i minus n i l a i space x space d i b a t a s i space p a d a space s e l a n g space left square bracket 0 comma 2 pi right square bracket comma space m a k a space l a k u k a n space u j i space t i t i k space d e n g a n space m e m i l i h space t i t i k space x space p a d a space s e l a n g space left square bracket 0 comma 2 pi right square bracket. space  J i k a space d i u j i space t i t i k space x equals pi comma space m a k a  open parentheses 2 cos invisible function application x plus square root of 3 close parentheses open parentheses 2 cos invisible function application x minus square root of 3 close parentheses equals open parentheses plus close parentheses open parentheses plus close parentheses equals open parentheses plus close parentheses  M e n g h a s i l k a n space b i l a n g a n space p o s i t i f comma space s e h i n g g a space d a e r a h space y a n g space m e n g a n d u n g space t i t i k space ? equals ? space b e r n i l a i space p o s i t i f. space  D a e r a h space y a n g space l a i n space a k a n space m e m i l i k i space tan d a space y a n g space b e r l a w a n a n space d e n g a n space d a e r a h space t e tan g g a n y a comma space s e h i n g g a

i v right parenthesis T e t a p k a n space d a e r a h space p e n y e l e s a i a n space  K a r e n a space p e r t i d a k s a m a a n space a k h i r space b e r b e n t u k  open parentheses 2 cos invisible function application x plus square root of 3 close parentheses open parentheses 2 cos invisible function application x minus square root of 3 close parentheses less or equal than 0  M a k a space d i p i l i h space d a e r a h minus d a e r a h space y a n g space b e r n i l a i space left parenthesis negative right parenthesis comma space y a i t u

S e h i n g g a space d i d a p a t space d a e r a h space p e n y e l e s a i a n  1 over 6 pi less or equal than x less or equal than 5 over 6 pi space a t a u space 7 over 6 pi less or equal than x less or equal than 11 over 6 pi  Y a n g space d a p a t space j u g a space d i t u l i s space s e b a g a i  open square brackets 1 over 6 pi comma 5 over 6 pi close square brackets union open square brackets 7 over 6 pi comma 11 over 6 pi close square brackets    v right parenthesis B a n d i n g k a n space d a e r a h space p e n y e l e s a i a n space  D a r i space p e r h i t u n g a n space d i d a p a t k a n space d a e r a h space p e n y e l e s a i a n space y a i t u space open square brackets 1 over 6 pi comma 5 over 6 pi close square brackets union open square brackets 7 over 6 pi comma 11 over 6 pi close square brackets  D a r i space s o a l space d i d a p a t k a n space d a e r a h space p e n y e l e s a i a n space y a i t u space left square bracket a comma b right square bracket union left square bracket c comma d right square bracket. space  M a k a  a equals 1 over 6 pi  b equals 5 over 6 pi  c equals 7 over 6 pi  d equals 11 over 6 pi  S e h i n g g a  a plus b plus c plus d equals 1 over 6 pi plus 5 over 6 pi plus 7 over 6 pi plus 11 over 6 pi equals 4 pi

44

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