Pertanyaan

Tentukan solusi yang mungkin dari setiap persamaan trigonometri di bawah ini. c. tan ( 3 x − 4 5 π ) = cotan x , 0 ≤ x ≤ 2 π

Tentukan solusi yang mungkin dari setiap persamaan trigonometri di bawah ini.

c. $tan (3 x - \frac{5 π}{4}) = cotan x, 0 \leq x \leq 2 π$

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Jawaban terverifikasi

Jawaban

himpunan penyelesaian dari persamaan tersebut adalah .

himpunan penyelesaian dari persamaan tersebut adalah HP equals open curly brackets 7 over 16 straight pi comma space 11 over 16 straight pi comma space 15 over 16 straight pi comma space 19 over 16 straight pi comma space 23 over 16 straight pi close curly brackets

HP equals open curly brackets 7 over 16 straight pi comma space 11 over 16 straight pi comma space 15 over 16 straight pi comma space 19 over 16 straight pi comma space 23 over 16 straight pi close curly brackets

Pembahasan

Penyelesaian dari persamaan trigonometri yaitu untuk setiap . Dengan demikian, himpunan penyelesaian dari persamaan tersebut adalah .

Penyelesaian dari persamaan trigonometri tan space x equals tan space alpha degree yaitu x equals open square brackets straight alpha plus open parentheses straight pi times straight k close parentheses close square brackets untuk setiap straight k element of bilangan space bulat .

$tan space open parentheses 3 straight x minus fraction numerator 5 straight pi over denominator 4 end fraction close parentheses equals cotan space straight x tan space open parentheses 3 straight x minus fraction numerator 5 straight pi over denominator 4 end fraction close parentheses equals tan space open parentheses straight pi over 2 minus straight x close parentheses space space space space space space space space space 3 straight x minus fraction numerator 5 straight pi over denominator 4 end fraction equals straight pi over 2 minus straight x plus open parentheses πk close parentheses space space space space space space space space space space space space space space 3 straight x plus straight x equals straight pi over 2 plus fraction numerator 5 straight pi over denominator 4 end fraction plus open parentheses πk close parentheses space space space space space space space space space space space space space space space space space space space space 4 straight x equals fraction numerator 2 straight pi over denominator 4 end fraction plus fraction numerator 5 straight pi over denominator 4 end fraction plus open parentheses πk close parentheses space space space space space space space space space space space space space space space space space space space space space 4 straight x equals fraction numerator 7 straight pi over denominator 4 end fraction plus open parentheses πk close parentheses straight x equals fraction numerator 7 straight pi over denominator 16 end fraction plus πk over 4 untuk space straight k equals 0 straight x equals fraction numerator 7 straight pi over denominator 16 end fraction plus πk over 4 straight x equals fraction numerator 7 straight pi over denominator 16 end fraction plus fraction numerator straight pi times 0 over denominator 4 end fraction straight x equals fraction numerator 7 straight pi over denominator 16 end fraction untuk space straight k equals 1 straight x equals fraction numerator 7 straight pi over denominator 16 end fraction plus πk over 4 straight x equals fraction numerator 7 straight pi over denominator 16 end fraction plus fraction numerator straight pi times 1 over denominator 4 end fraction straight x equals fraction numerator 7 straight pi over denominator 16 end fraction plus fraction numerator 4 straight pi over denominator 16 end fraction straight x equals fraction numerator 11 straight pi over denominator 16 end fraction untuk space straight k equals 2 straight x equals fraction numerator 7 straight pi over denominator 16 end fraction plus πk over 4 straight x equals fraction numerator 7 straight pi over denominator 16 end fraction plus fraction numerator straight pi times 2 over denominator 4 end fraction straight x equals fraction numerator 7 straight pi over denominator 16 end fraction plus fraction numerator 8 straight pi over denominator 16 end fraction straight x equals 15 over 16 straight pi untuk space straight k equals 3 straight x equals fraction numerator 7 straight pi over denominator 16 end fraction plus πk over 4 straight x equals fraction numerator 7 straight pi over denominator 16 end fraction plus fraction numerator straight pi times 3 over denominator 4 end fraction straight x equals fraction numerator 7 straight pi over denominator 16 end fraction plus fraction numerator 12 straight pi over denominator 16 end fraction x equals 19 over 16 straight pi untuk space straight k equals 4 straight x equals fraction numerator 7 straight pi over denominator 16 end fraction plus πk over 4 straight x equals fraction numerator 7 straight pi over denominator 16 end fraction plus fraction numerator straight pi times 4 over denominator 4 end fraction straight x equals fraction numerator 7 straight pi over denominator 16 end fraction plus fraction numerator 16 straight pi over denominator 16 end fraction straight x equals 23 over 16 straight pi$

Dengan demikian, himpunan penyelesaian dari persamaan tersebut adalah HP equals open curly brackets 7 over 16 straight pi comma space 11 over 16 straight pi comma space 15 over 16 straight pi comma space 19 over 16 straight pi comma space 23 over 16 straight pi close curly brackets .