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Tentukan HP untuk nilai x yang memenuhi masing-masing persamaan berikut. e. cos 2 ( 2 x + 10 ) ∘ = 0 , 2 , untuk 0 ∘ ≤ x < 36 0 ∘

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

e. , untuk  

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S. Yoga

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

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Pembahasan

Ingat bahwa: Sehingga, Jadi,nilai HPyang memenuhi persamaan tersebut pada interval adalah .

Ingat bahwa:

  • cos space left parenthesis negative x right parenthesis degree equals cos space x degree  

Sehingga, 

table attributes columnalign right center left columnspacing 0px end attributes row cell cos squared open parentheses 2 x plus 10 close parentheses degree end cell equals cell 0 comma 2 end cell row cell cos open parentheses 2 x plus 10 close parentheses degree end cell equals cell plus-or-minus square root of 0 comma 2 end root end cell end table 

cos open parentheses 2 x plus 10 close parentheses degree equals square root of 0 comma 2 end root space atau thin space cos open parentheses 2 x plus 10 close parentheses degree equals negative square root of 0 comma 2 end root  

table attributes columnalign right center left columnspacing 0px end attributes row blank rightwards arrow cell cos open parentheses 2 x plus 10 close parentheses degree equals square root of 0 comma 2 end root end cell row blank rightwards arrow cell 2 x plus 10 degree equals cos to the power of negative 1 end exponent open parentheses square root of 0 comma 2 end root close parentheses plus 360 degree n end cell row cell 2 x end cell equals cell cos to the power of negative 1 end exponent open parentheses square root of 0 comma 2 end root close parentheses plus 360 degree n minus 10 degree end cell row x equals cell 180 degree n minus 5 degree plus 31 comma 72 degree end cell row x equals cell 26 comma 72 degree plus 180 degree n end cell row cell Untuk space n end cell equals cell left curly bracket 0 comma space 1 right curly bracket end cell row x equals cell open curly brackets 26 comma 72 degree semicolon space 206 comma 72 degree close curly brackets end cell row blank blank blank row blank rightwards arrow cell 2 x plus 10 degree equals 360 degree minus cos to the power of negative 1 end exponent open parentheses square root of 0 comma 2 end root close parentheses plus 360 degree n end cell row x equals cell 180 degree plus 180 degree n minus 5 degree minus 31 comma 72 degree end cell row x equals cell 143 comma 28 degree plus 180 degree n end cell row cell Untuk space n end cell equals cell left curly bracket 0 comma space 1 right curly bracket end cell row x equals cell open curly brackets 143 comma 28 degree semicolon space 323 comma 28 degree close curly brackets end cell end table 


table attributes columnalign right center left columnspacing 0px end attributes row blank rightwards arrow cell cos open parentheses 2 x plus 10 close parentheses degree equals negative square root of 0 comma 2 end root end cell row blank rightwards arrow cell 2 x plus 10 degree equals cos to the power of negative 1 end exponent open parentheses negative square root of 0 comma 2 end root close parentheses plus 360 degree n end cell row cell 2 x end cell equals cell cos open parentheses negative square root of 0 comma 2 end root close parentheses plus 360 degree n minus 10 degree end cell row x equals cell 180 degree n minus 5 degree plus 58 comma 28 degree end cell row x equals cell 53 comma 28 degree plus 180 degree n end cell row cell Untuk space n end cell equals cell left curly bracket 0 comma space 1 right curly bracket end cell row x equals cell open curly brackets 53 comma 28 degree semicolon space 233 comma 28 degree close curly brackets end cell row blank blank blank row blank rightwards arrow cell 2 x plus 10 degree equals negative cos to the power of negative 1 end exponent open parentheses negative square root of 0 comma 2 end root close parentheses plus 360 degree n end cell row cell 2 x end cell equals cell negative cos to the power of negative 1 end exponent open parentheses negative square root of 0 comma 2 end root close parentheses plus 360 degree n minus 10 degree end cell row x equals cell 180 to the power of ring operator thin space end exponent n minus 5 to the power of ring operator thin space end exponent minus 58 comma 28 degree end cell row x equals cell negative 63 comma 28 to the power of ring operator thin space end exponent 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 116 comma 72 degree semicolon space 296 comma 72 degree close curly brackets end cell end table 

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

HP equals open curly brackets 26 comma 72 degree semicolon space 206 comma 72 degree semicolon space 143 comma 28 degree semicolon space 323 comma 28 degree semicolon space 53 comma 28 degree semicolon space 233 comma 28 degree semicolon space 116 comma 72 degree semicolon space 296 comma 72 degree close curly brackets.

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