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Tentukan semua sudut antara 0∘ dan 360∘ yang memenuhi persamaan berikut. d. 3 tan2 x+5 secan x+1=0

Pertanyaan

Tentukan semua sudut antara 0 degree space dan space 360 degree yang memenuhi persamaan berikut.

d. 3 space tan squared space x plus 5 space secan space x plus 1 equals 0 

S. Yoga

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

 semua sudut antara 0 degree space dan space 360 degree yang memenuhi persamaan tersebut adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open curly brackets 153 comma 43 degree semicolon space 333 comma 43 degree semicolon space 71 comma 57 degree semicolon space 251 comma 57 degree close curly brackets end cell end table.

Pembahasan

Ingat bahwa:

  • tan space left parenthesis 180 minus x right parenthesis degree equals tan space x degree  

Sehingga, 

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 tan squared open parentheses x close parentheses plus 5 sec open parentheses x close parentheses plus 1 end cell equals 0 row cell 1 plus 3 open parentheses sec squared open parentheses x close parentheses minus 1 close parentheses plus 5 sec open parentheses x close parentheses end cell equals 0 row cell 3 sec squared open parentheses x close parentheses plus 5 sec open parentheses x close parentheses minus 2 end cell equals 0 row cell open parentheses 3 sec open parentheses x close parentheses minus 1 close parentheses open parentheses sec open parentheses x close parentheses plus 2 close parentheses end cell equals 0 end table 

table attributes columnalign right center left columnspacing 0px end attributes row cell sec open parentheses x close parentheses end cell equals cell 1 third comma thin space sec open parentheses x close parentheses equals negative 2 end cell row cell fraction numerator 1 over denominator tan open parentheses x close parentheses end fraction end cell equals cell 1 third comma thin space fraction numerator 1 over denominator tan open parentheses x close parentheses end fraction equals negative 2 end cell end table 


table attributes columnalign right center left columnspacing 0px end attributes row blank rightwards arrow cell space space space space space space space space space fraction numerator 1 over denominator tan open parentheses x close parentheses end fraction equals 1 third end cell row 3 equals cell tan open parentheses x close parentheses end cell row cell tan open parentheses x close parentheses end cell equals 3 row blank rightwards arrow cell x equals tan to the power of negative 1 end exponent open parentheses 3 close parentheses plus 180 degree n end cell row x equals cell 71 comma 57 degree plus 180 degree n end cell row cell Untuk space n end cell equals cell left curly bracket 1 comma space 2 right curly bracket end cell row x equals cell open curly brackets 71 comma 57 degree semicolon space 251 comma 57 degree close curly brackets end cell row blank blank blank row blank rightwards arrow cell space space space space space space space space space fraction numerator 1 over denominator tan open parentheses x close parentheses end fraction equals negative 2 end cell row cell fraction numerator 1 over denominator tan open parentheses x close parentheses end fraction tan open parentheses x close parentheses end cell equals cell negative 2 tan open parentheses x close parentheses end cell row 1 equals cell negative 2 tan open parentheses x close parentheses end cell row cell negative 2 tan open parentheses x close parentheses end cell equals 1 row cell tan open parentheses x close parentheses end cell equals cell negative 1 half end cell row x equals cell tan open parentheses negative 1 half close parentheses plus 180 degree n end cell row x equals cell negative 26 comma 57 degree plus 180 degree n end cell row cell Untuk space n end cell equals cell left curly bracket 1 comma space 2 right curly bracket end cell row x equals cell open curly brackets 153 comma 43 degree semicolon space 333 comma 43 degree close curly brackets end cell end table   

Jadi, semua sudut antara 0 degree space dan space 360 degree yang memenuhi persamaan tersebut adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open curly brackets 153 comma 43 degree semicolon space 333 comma 43 degree semicolon space 71 comma 57 degree semicolon space 251 comma 57 degree close curly brackets end cell end table.

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