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Tentukan semua nilai x dalam interval − 18 0 ∘ ≤ x ≤ 18 0 ∘ dari masing-masing persamaan trigonometri berikut. f. tan 5 x ∘ = 0 , 8

Tentukan semua nilai x dalam interval  dari masing-masing persamaan trigonometri berikut. 

f. 

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A. Khairunisa

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Pembahasan

Terdapat tiga langkah untuk menentukan HP dari persamaan tersebut. 1. Langkah 1 : 2. Langkah 2: Perhatikan perhitungan berikut. Misalkan , maka selang interval persamaan tersebut menjadi . Langkah 1 Langkah 2 Ubah a ke dalam x. Dengan demikian, semua nilai yang memenuhi persamaan tersebut adalah

Terdapat tiga langkah untuk menentukan HP dari persamaan tersebut.

1. Langkah 1 : tan to the power of negative 1 end exponent space open parentheses straight a close parentheses

2. Langkah 2 : tan space open parentheses 180 plus-or-minus straight a close parentheses degree equals tan space straight a degree

Perhatikan perhitungan berikut.

Misalkan straight a equals 5 straight x, maka selang interval persamaan tersebut menjadi negative 900 degree less or equal than straight a less or equal than 900 degree.

Langkah 1

table attributes columnalign right center left columnspacing 0px end attributes row cell tan to the power of negative 1 end exponent space open parentheses straight a close parentheses end cell equals cell tan to the power of negative 1 end exponent space open parentheses 0.8 close parentheses end cell row blank almost equal to cell 38 comma 66 degree end cell end table

Langkah 2

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space straight a degree end cell equals cell tan space open parentheses straight a plus 180 close parentheses degree end cell row straight a equals cell open parentheses 38 comma 66 plus 180 close parentheses degree end cell row straight a equals cell 218 comma 66 degree end cell row blank blank blank row cell tan space straight a degree end cell equals cell tan space open parentheses straight a plus 180 close parentheses degree end cell row straight a equals cell open parentheses 218 comma 66 plus 180 close parentheses degree end cell row straight a equals cell 398 comma 66 degree end cell row blank blank blank row cell tan space straight a degree end cell equals cell tan space open parentheses straight a plus 180 close parentheses degree end cell row straight a equals cell open parentheses 398 comma 66 plus 180 close parentheses degree end cell row straight a equals cell 578 comma 66 degree end cell row blank blank blank row cell tan space straight a degree end cell equals cell tan space open parentheses straight a plus 180 close parentheses degree end cell row straight a equals cell open parentheses 578 comma 66 plus 180 close parentheses degree end cell row straight a equals cell 758 comma 66 degree end cell row blank blank blank row cell tan space straight a degree end cell equals cell tan space open parentheses straight a minus 180 close parentheses degree end cell row straight a equals cell open parentheses 38 comma 66 minus 180 close parentheses degree end cell row straight a equals cell negative 141 comma 34 degree end cell row blank blank blank row cell tan space straight a degree end cell equals cell tan space open parentheses straight a minus 180 close parentheses degree end cell row straight a equals cell open parentheses negative 141 comma 34 minus 180 close parentheses degree end cell row straight a equals cell negative 321 comma 34 degree end cell row blank blank blank row cell tan space straight a degree end cell equals cell tan space open parentheses straight a minus 180 close parentheses degree end cell row straight a equals cell open parentheses negative 321 comma 34 minus 180 close parentheses degree end cell row straight a equals cell negative 501 comma 34 degree end cell row blank blank blank row cell tan space straight a degree end cell equals cell tan space open parentheses straight a minus 180 close parentheses degree end cell row straight a equals cell open parentheses negative 501 comma 34 minus 180 close parentheses degree end cell row straight a equals cell negative 681 comma 34 degree end cell row blank blank blank row cell tan space straight a degree end cell equals cell tan space open parentheses straight a minus 180 close parentheses degree end cell row straight a equals cell open parentheses negative 681 comma 34 minus 180 close parentheses degree end cell row straight a equals cell negative 861 comma 34 degree end cell end table

Ubah a ke dalam x.

straight a equals 5 straight x straight x equals 1 fifth straight a  untuk space straight a equals negative 861 comma 34 degree straight x equals 1 fifth open parentheses negative 861 comma 34 degree close parentheses straight x equals negative 172 comma 268 degree  untuk space straight a equals negative 681 comma 34 degree straight x equals 1 fifth open parentheses negative 681 comma 34 degree close parentheses straight x equals negative 136 comma 268 degree  untuk space straight a equals negative 501 comma 34 degree straight x equals 1 fifth open parentheses negative 501 comma 34 degree close parentheses straight x equals negative 100 comma 268 degree  untuk space straight a equals negative 321 comma 34 degree straight x equals 1 fifth open parentheses negative 321 comma 34 degree close parentheses straight x equals negative 64 comma 268 degree  untuk space straight a equals negative 141 comma 34 degree straight x equals 1 fifth open parentheses negative 141 comma 34 degree close parentheses straight x equals negative 28 comma 268 degree  untuk space straight a equals 38 comma 66 degree straight x equals 1 fifth open parentheses 38 comma 66 degree close parentheses straight x equals 7 comma 732 degree  untuk space straight a equals 218 comma 66 degree straight x equals 1 fifth open parentheses 218 comma 66 degree close parentheses straight x equals 43 comma 732 degree  untuk space straight a equals 398 comma 66 degree straight x equals 1 fifth open parentheses 398 comma 66 degree close parentheses straight x equals 79 comma 732 degree  untuk space straight a equals 578 comma 66 degree straight x equals 1 fifth open parentheses 578 comma 66 degree close parentheses straight x equals 115 comma 732 degree  untuk space straight a equals 758 comma 66 degree straight x equals 1 fifth open parentheses 758 comma 66 degree close parentheses straight x equals 151 comma 732 degree

Dengan demikian, semua nilai yang memenuhi persamaan tersebut adalah x equals left curly bracket negative 171 comma 268 degree semicolon space minus 136 comma 268 degree semicolon space minus 100 comma 268 degree semicolon space minus 64 comma 268 degree semicolon space space space space space space space space space space space minus 28 comma 268 degree semicolon space 7 comma 732 degree semicolon space 43 comma 732 degree semicolon space 79 comma 732 degree semicolon space 115 comma 732 degree semicolon space space space space space space space space space space space 151 comma 732 degree right curly bracket.

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