Roboguru

Tentukan nilai x, untuk  jika

Pertanyaan

Tentukan nilai x, untuk 0 degree less or equal than x less or equal than 360 degree jika sec space x equals 2 over 3 square root of 3  

Pembahasan Soal:

Diketahui : sec space x equals 2 over 3 square root of 30 degree less or equal than x less or equal than 360 degree

table attributes columnalign right center left columnspacing 0px end attributes row cell sec space straight x end cell equals cell 2 over 3 square root of 3 end cell row cell fraction numerator 1 over denominator cos space straight x end fraction end cell equals cell fraction numerator 2 square root of 3 over denominator 3 end fraction end cell row cell cos space straight x end cell equals cell fraction numerator 3 over denominator 2 square root of 3 end fraction end cell row cell cos space straight x end cell equals cell fraction numerator 3 square root of 3 over denominator 2 cross times 3 end fraction end cell row cell cos space straight x end cell equals cell fraction numerator square root of 3 over denominator 2 end fraction end cell row cell cos space straight x end cell equals cell cos space 30 end cell row straight x equals cell 30 degree end cell end table 

Dengan menggunakan rumus persamaan trigonometri cos space x equals cos space a rightwards double arrow x subscript 1 comma 2 end subscript equals plus-or-minus a plus k cross times 2 straight pi maka

Untuk k = 0space 

table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 end cell equals cell 30 plus 0 cross times 360 end cell row blank equals cell 30 degree end cell row blank blank blank row cell x subscript 2 end cell equals cell negative 30 plus 0 cross times 360 end cell row blank equals cell negative 30 degree end cell end table 

Untuk k = 1

table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 end cell equals cell 30 plus 1 cross times 360 end cell row blank equals cell 390 degree end cell row blank blank blank row cell x subscript 2 end cell equals cell negative 30 plus 1 cross times 360 end cell row blank equals cell 330 degree end cell row blank blank blank end table 

Jadi, nilai x untuk 0 degree less or equal than x less or equal than 360 degree jika sec space x equals 2 over 3 square root of 3  adalah left curly bracket 30 degree comma space 330 degree right curly bracket 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 20 Mei 2021

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