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Pertanyaan

Penyelesaian dari persamaan 2 space sin space open parentheses x plus 1 half straight pi close parentheses times sin space x equals 1 comma space 0 less or equal than x less or equal than straight pi adalah...

  1. 1 fourth straight pi

  2. 1 half straight pi

  3. 3 over 4 straight pi

  4. straight pi

  5. 5 over 12 straight pi

M. Nasrullah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Pembahasan

Ingat kembali:

2 sin space A times cos space B equals negative cos space open parentheses A plus B close parentheses plus cos space open parentheses A minus B close parentheses 

cos space open parentheses 180 minus a close parentheses equals negative cos space a

cos space 0 degree equals 1

Sehingga diperoleh perhitungan:

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 space sin space open parentheses x plus 1 half straight pi close parentheses times sin space x end cell equals 1 row cell negative cos space open parentheses x plus 90 degree plus straight x close parentheses plus cos space open parentheses x plus 90 degree minus straight x close parentheses end cell equals 1 row cell negative cos space open parentheses 2 x plus 90 degree close parentheses plus cos space 90 degree end cell equals 1 row cell negative cos space space open parentheses 2 x plus 90 degree close parentheses end cell equals 1 row cell cos space space open parentheses 2 x plus 90 degree close parentheses end cell equals cell negative 1 end cell row cell cos space space open parentheses 2 x plus 90 degree close parentheses end cell equals cell negative cos space 0 end cell row cell cos space space open parentheses 2 x plus 90 degree close parentheses end cell equals cell cos space open parentheses 180 minus 0 close parentheses end cell row cell cos space space open parentheses 2 x plus 90 degree close parentheses end cell equals cell cos space 180 end cell end table

Solusi I

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x plus 90 end cell equals cell 180 plus k times 360 end cell row cell 2 x end cell equals cell 90 plus k times 360 end cell row x equals cell 45 plus k times 180 end cell row blank blank blank row k equals 0 row cell x subscript 1 end cell equals cell 45 plus 0 end cell row cell x subscript 1 end cell equals 45 row cell x subscript 1 end cell equals cell 45 over 180 straight pi end cell row cell straight x subscript 1 end cell equals cell 1 fourth straight pi end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x plus 90 end cell equals cell negative 180 plus k times 360 end cell row cell 2 x end cell equals cell negative 90 plus k times 360 end cell row x equals cell negative 45 plus k times 180 end cell row blank blank blank row k equals 1 row cell x subscript 2 end cell equals cell negative 45 plus 180 end cell row cell x subscript 2 end cell equals 135 row cell x subscript 2 end cell equals cell 135 over 180 straight pi end cell row cell straight x subscript 2 end cell equals cell 3 over 4 straight pi end cell end table

Dengan mikian, persamaan tersebut adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open curly brackets 1 fourth straight pi comma space 3 over 4 straight pi close curly brackets end cell end table

Jadi,  jawaban yang tepat adalah A dan C

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