Pertanyaan

Tentukan semua sudut dalam 0 ≤ θ ≤ 2 π yang memenuhi persamaan berikut. e. 3 sin θ − cos θ = 0

Tentukan semua sudut dalam $0 \leq θ \leq 2 π$ yang memenuhi persamaan berikut.

e. $3 sin θ - cos θ = 0$

E. Nur

Master Teacher

Mahasiswa/Alumni Institut Teknologi Sepuluh Nopember

Jawaban terverifikasi

Jawaban

karena maka .

karena

0 less or equal than theta less or equal than 2 straight pi

maka $HP equals open curly brackets straight pi over 6 comma fraction numerator 7 straight pi over denominator 6 end fraction close curly brackets$ .

Pembahasan

Ingat! Perhatikan perhitungan berikut ini! Dengan demikian karena maka .

Ingat!

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space x end cell equals cell tan space p end cell row x equals cell p plus k times straight pi end cell end table

Perhatikan perhitungan berikut ini!

$table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 3 space sin space theta minus cos space theta end cell equals 0 row cell square root of 3 space sin space theta end cell equals cell cos space theta end cell row cell fraction numerator sin space theta over denominator cos space theta end fraction end cell equals cell fraction numerator 1 over denominator square root of 3 end fraction end cell row cell tan space theta end cell equals cell space 1 third square root of 3 end cell row cell tan space theta end cell equals cell tan space straight pi over 6 end cell row blank blank blank row theta equals cell straight pi over 6 plus k times straight pi end cell row theta equals cell straight pi over 6 comma fraction numerator 7 straight pi over denominator 6 end fraction comma space... end cell end table$

Dengan demikian karena 0 less or equal than theta less or equal than 2 straight pi maka $HP equals open curly brackets straight pi over 6 comma fraction numerator 7 straight pi over denominator 6 end fraction close curly brackets$ .