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Untuk 0∘≤θ≤360∘, carilah nilai θ yang memenuhi masing-masing persamaan berikut. f. tan2 θ∘=cos θ∘1​+1

Pertanyaan

Untuk 0 degree less or equal than theta less or equal than 360 degree, carilah nilai theta yang memenuhi masing-masing persamaan berikut.

f. tan squared space theta degree equals fraction numerator 1 over denominator cos space theta degree end fraction plus 1 

S. Yoga

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Pembahasan

Ingat bahwa:

  • fraction numerator 1 over denominator cos space x end fraction equals s e c space x 

Sehingga, 

table attributes columnalign right center left columnspacing 0px end attributes row cell tan squared space theta degree end cell equals cell fraction numerator 1 over denominator cos space theta degree end fraction plus 1 end cell row cell tan squared open parentheses theta close parentheses end cell equals cell sec open parentheses theta close parentheses plus 1 end cell row cell tan squared open parentheses theta close parentheses minus sec open parentheses theta close parentheses minus 1 end cell equals 0 row cell negative 1 minus sec open parentheses theta close parentheses plus sec squared open parentheses theta close parentheses minus 1 end cell equals 0 row cell negative 2 minus sec open parentheses theta close parentheses plus sec squared open parentheses theta close parentheses end cell equals 0 row cell sec open parentheses theta close parentheses end cell equals cell 2 comma thin space sec open parentheses theta close parentheses equals negative 1 end cell end table  

table attributes columnalign right center left columnspacing 0px end attributes row blank rightwards arrow cell sec open parentheses theta close parentheses equals 2 end cell row blank rightwards arrow cell theta equals 60 degree plus 360 degree n end cell row cell Untuk space n end cell equals 0 row theta equals cell 60 degree end cell row blank blank blank row blank rightwards arrow cell theta equals 300 degree plus 360 degree n end cell row cell Untuk space n end cell equals 0 row theta equals cell 300 degree end cell end table 

table attributes columnalign right center left columnspacing 0px end attributes row blank rightwards arrow cell sec open parentheses theta close parentheses equals negative 1 end cell row blank rightwards arrow cell theta equals 180 degree plus 360 degree n end cell row cell Untuk space n end cell equals 0 row theta equals cell 180 degree end cell end table 

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

theta equals open curly brackets 60 degree comma thin space 300 degree comma thin space 180 degree close curly brackets.

177

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Pertanyaan serupa

Selesaikanlah persamaan berikut untuk 0∘<x<360∘ cos2 x−3sin x⋅cos x+2sin2 x=0

87

5.0

Jawaban terverifikasi

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