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Tentukan HP untuk nilai x yang memenuhi masing-masing persamaan berikut. d. sin2 (x+15)∘=0,6, untuk 0∘<x≤360∘

Pertanyaan

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

d. sin squared space left parenthesis x plus 15 right parenthesis degree equals 0 comma 6, untuk 0 degree less than x less or equal than 360 degree 

S. Yoga

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

 nilai HP yang memenuhi persamaan tersebut pada interval 0 degree less than x less or equal than 360 degree adalah HP equals left curly bracket 35 comma 77 degree semicolon space 144 comma 23 degree semicolon space 215 comma 77 degree semicolon space 294 comma 23 degree right curly bracket.

Pembahasan

Ingat bahwa:

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

Sehingga, 

table attributes columnalign right center left columnspacing 0px end attributes row cell sin squared open parentheses x plus 15 close parentheses degree end cell equals cell 0 comma 6 end cell row cell sin open parentheses x plus 15 close parentheses degree end cell equals cell plus-or-minus square root of 0 comma 6 end root end cell end table 
sin open parentheses x plus 15 close parentheses degree equals square root of 0 comma 6 end root space atau thin space sin open parentheses x plus 15 thin space degree close parentheses equals negative square root of 0 comma 6 end root  

table attributes columnalign right center left columnspacing 0px end attributes row blank rightwards arrow cell sin open parentheses x plus 15 close parentheses degree equals square root of 0 comma 6 end root end cell row blank rightwards arrow cell x plus 15 degree equals sin to the power of negative 1 end exponent open parentheses square root of 0 comma 6 end root close parentheses plus 360 degree n end cell row x equals cell sin to the power of negative 1 end exponent open parentheses square root of 0 comma 6 end root close parentheses plus 360 degree n minus 15 degree end cell row x equals cell 50 comma 77 degree plus 360 degree n minus 15 degree end cell row x equals cell 35 comma 77 degree plus 360 degree n end cell row cell Untuk space n end cell equals 0 row x equals cell 35 comma 77 degree end cell row blank blank blank row blank rightwards arrow cell x plus 15 degree equals 180 degree minus sin to the power of negative 1 end exponent open parentheses square root of 0 comma 6 end root close parentheses plus 360 degree n end cell row x equals cell 180 degree minus 50 comma 77 degree plus 360 degree n minus 15 degree end cell row x equals cell 114 comma 23 degree plus 360 degree n end cell row cell Untuk space n end cell equals 0 row x equals cell 114 comma 23 degree end cell end table 


table attributes columnalign right center left columnspacing 0px end attributes row blank rightwards arrow cell sin open parentheses x plus 15 close parentheses degree equals negative square root of 0 comma 6 end root end cell row blank rightwards arrow cell x plus 15 degree equals sin to the power of negative 1 end exponent open parentheses negative square root of 0 comma 6 end root close parentheses plus 360 degree n end cell row x equals cell negative sin to the power of negative 1 end exponent open parentheses square root of 3 over 5 end root close parentheses plus 360 degree n minus 15 degree end cell row x equals cell negative 50 comma 77 degree plus 360 degree n minus 15 degree end cell row x equals cell negative 65 comma 77 degree plus 360 degree n end cell row cell Untuk space n end cell equals 1 row x equals cell 294 comma 23 degree end cell row blank blank blank row blank rightwards arrow cell x plus 15 degree equals 180 degree plus sin to the power of negative 1 end exponent open parentheses square root of 0 comma 6 end root close parentheses plus 360 degree n end cell row x equals cell 180 degree plus sin to the power of negative 1 end exponent open parentheses square root of 0 comma 6 end root close parentheses plus 360 degree n minus 15 degree end cell row x equals cell 180 degree plus 50 comma 77 degree plus 360 degree n minus 15 degree end cell row x equals cell 215 comma 77 degree plus 360 degree n end cell row cell Untuk space n end cell equals 0 row x equals cell 215 comma 77 degree end cell end table 

Jadi, nilai HP yang memenuhi persamaan tersebut pada interval 0 degree less than x less or equal than 360 degree adalah HP equals left curly bracket 35 comma 77 degree semicolon space 144 comma 23 degree semicolon space 215 comma 77 degree semicolon space 294 comma 23 degree right curly bracket.

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Tentukan HP untuk nilai x yang memenuhi masing-masing persamaan berikut. b. 6 sin2 x=5 sin x− 1, untuk 0∘≤x≤180∘

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