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Pertanyaan

Tentukan HP untuk nilai x yang memenuhi masing-masing persamaan berikut.

a. 3 space sin space x plus 3 space cos space x equals fraction numerator 1 over denominator cos space x minus sin space x end fraction, untuk 0 degree less or equal than x less or equal than 360 degree 

S. Yoga

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Pembahasan

Ingat bahwa:

  • sin space left parenthesis 180 minus x right parenthesis degree equals sin space x degree 
  • cos squared space x equals 1 minus sin squared space x 

Sehingga, 

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell 3 sin open parentheses x close parentheses plus 3 cos open parentheses x close parentheses end cell equals cell fraction numerator 1 over denominator cos open parentheses x close parentheses minus sin open parentheses x close parentheses end fraction end cell row cell 3 sin open parentheses x close parentheses plus 3 cos open parentheses x close parentheses minus fraction numerator 1 over denominator cos open parentheses x close parentheses minus sin open parentheses x close parentheses end fraction end cell equals 0 row cell fraction numerator negative 3 sin squared open parentheses x close parentheses plus 3 cos squared open parentheses x close parentheses minus 1 over denominator cos open parentheses x close parentheses minus sin open parentheses x close parentheses end fraction end cell equals cell 0 space open parentheses fraction numerator f open parentheses x close parentheses over denominator g open parentheses x close parentheses end fraction equals 0 rightwards double arrow f open parentheses x close parentheses equals 0 close parentheses end cell row cell negative 3 sin squared open parentheses x close parentheses plus 3 cos squared open parentheses x close parentheses minus 1 end cell equals 0 row cell negative 1 plus 3 cos squared open parentheses x close parentheses minus 3 sin squared open parentheses x close parentheses end cell equals 0 row cell negative 1 plus 3 open parentheses 1 minus sin squared open parentheses x close parentheses close parentheses minus 3 sin squared open parentheses x close parentheses end cell equals 0 row cell 2 minus 6 sin squared open parentheses x close parentheses end cell equals 0 row cell sin squared open parentheses x close parentheses end cell equals cell fraction numerator negative 2 over denominator negative 6 end fraction end cell row cell sin left parenthesis x right parenthesis end cell equals cell 1 third end cell row cell sin open parentheses x close parentheses end cell equals cell square root of 1 third end root comma thin space sin open parentheses x close parentheses equals negative square root of 1 third end root end cell end table end style   

table attributes columnalign right center left columnspacing 0px end attributes row blank rightwards arrow cell sin open parentheses x close parentheses equals square root of 1 third end root end cell row blank rightwards arrow cell x equals sin to the power of negative 1 end exponent open parentheses square root of 1 third end root close parentheses plus 360 degree n end cell row x equals cell 35 comma 26 degree plus 360 degree n end cell row cell Untuk space n end cell equals 0 row x equals cell 35 comma 26 degree end cell row blank blank blank row blank rightwards arrow cell x equals 180 degree minus sin to the power of negative 1 end exponent open parentheses square root of 1 third end root close parentheses plus 360 degree n end cell row x equals cell 180 degree minus 35 comma 26 degree plus 360 degree n end cell row x equals cell 144 comma 74 degree plus 360 degree n end cell row cell Untuk space n end cell equals 0 row x equals cell 144 comma 74 degree end cell end table  

table attributes columnalign right center left columnspacing 0px end attributes row blank rightwards arrow cell sin open parentheses x close parentheses equals negative square root of 1 third end root end cell row blank rightwards arrow cell x equals 180 degree plus sin to the power of negative 1 end exponent open parentheses square root of 1 third end root close parentheses plus 360 degree n end cell row x equals cell 180 degree plus 35 comma 26 degree plus 360 degree n end cell row x equals cell 215 comma 26 degree plus 360 degree n end cell row cell untuk space x end cell equals 0 row x equals cell 215 comma 26 degree end cell row blank blank blank row blank rightwards arrow cell x equals negative sin to the power of negative 1 end exponent open parentheses square root of 1 third end root close parentheses plus 360 degree n end cell row x equals cell negative 35 comma 26 degree plus 360 degree n end cell row cell untuk space n end cell equals 1 row x equals cell 324 comma 74 degree end cell end table 

Jadi, nilai HP yang memenuhi persamaan tersebut pada interval 0 degree less or equal than x less or equal than 360 degree adalah 

HP equals left curly bracket 35 comma 26 degree semicolon space 144 comma 74 degree semicolon space 215 comma 26 degree semicolon space 324 comma 74 degree right curly bracket.

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