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Carilah himpunan penyelesaian dari persamaan-persamaan berikut: b. tan2x∘−4 tan x∘=0; −180∘≤x≤180∘

Pertanyaan

Carilah himpunan penyelesaian dari persamaan-persamaan berikut:

b. begin mathsize 14px style tan squared x degree minus 4 space tan space x degree equals 0 semicolon space minus 180 degree less or equal than x less or equal than 180 degree end style 

S. Amamah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

himpunan penyelesaian  begin mathsize 14px style tan squared x degree minus 4 space tan space x degree equals 0 semicolon space minus 180 degree less or equal than x less or equal than 180 degree end style  adalah begin mathsize 14px style left curly bracket 0 degree comma space 76 degree comma space 180 degree right curly bracket end style.

Pembahasan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan squared x degree minus 4 space tan space x degree end cell equals 0 row cell tan space x open parentheses tan space x minus 4 close parentheses end cell equals 0 end table end style

hal itu berarti  begin mathsize 14px style tan space x degree equals 0 space atau space tan space x degree equals 4 end style sehingga:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan space x degree end cell equals 0 row cell tan space x degree end cell equals cell tan space 0 degree end cell row x equals cell 0 degree plus k times 180 degree end cell row k equals cell 0 rightwards arrow x equals 0 degree plus open parentheses 0 close parentheses times 180 degree equals 0 degree end cell row k equals cell 1 rightwards arrow x equals 0 degree plus open parentheses 1 close parentheses times 180 degree equals 180 degree end cell row k equals cell 2 rightwards arrow x equals 0 degree plus open parentheses 2 close parentheses times 180 degree equals 360 degree space open parentheses Tidak space memenuhi close parentheses end cell end table end style   

dan 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan space x degree end cell equals 4 row cell tan space x degree end cell equals cell tan space 76 degree space open parentheses tan space 76 almost equal to 4 comma 01 close parentheses end cell row x equals cell 76 degree plus k times 180 degree end cell row k equals cell 0 rightwards arrow x equals 76 degree plus left parenthesis 0 right parenthesis times 180 degree equals 76 degree end cell row k equals cell 1 rightwards arrow x equals 76 degree plus left parenthesis 1 right parenthesis times 180 degree equals 256 degree space left parenthesis Tidak space memenuhi right parenthesis end cell end table end style 

Jadi, himpunan penyelesaian  begin mathsize 14px style tan squared x degree minus 4 space tan space x degree equals 0 semicolon space minus 180 degree less or equal than x less or equal than 180 degree end style  adalah begin mathsize 14px style left curly bracket 0 degree comma space 76 degree comma space 180 degree right curly bracket end style.

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