Tentukan 5 perbandingan yang lain jika diketahui cos β=q!

Pertanyaan

Tentukan $5$ perbandingan yang lain jika diketahui $\cos\;\beta=q$ !

R. Hajrianti

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

perbandingan trigonometri yang lain yaitu sin space beta equals square root of 1 minus q squared end root

, $tan space beta equals fraction numerator square root of 1 minus q squared end root over denominator q end fraction$ , sec space beta equals 1 over q

, $cosec space beta equals fraction numerator square root of 1 minus q squared end root over denominator 1 minus q squared end fraction$ , dan $c o t space beta equals fraction numerator q square root of 1 minus q squared end root over denominator square root of 1 minus q squared end root end fraction$ .

Pembahasan

Diketahui cos space beta equals q . Dengan menggunakan definisi cosinus maka diperoleh:

$table attributes columnalign right center left columnspacing 0px end attributes row cell cos space beta end cell equals q row cell cos space beta end cell equals cell q over 1 end cell row cell fraction numerator sisi space samping over denominator sisi space miring end fraction end cell equals cell q over 1 end cell row blank blank blank end table$

Kemudian, dengan menggunakan teorema pythagoras diperoleh sisi depan sebagai berikut.

Berdasarkan uraian di atas, maka diperoleh perbandingan trigonometri yang lain sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell sin space beta end cell equals cell fraction numerator sisi space depan over denominator sisi space miring end fraction end cell row blank equals cell fraction numerator square root of 1 minus q squared end root over denominator 1 end fraction end cell row blank equals cell square root of 1 minus q squared end root end cell end table$

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan space beta end cell equals cell fraction numerator sisi space depan over denominator sisi space samping end fraction end cell row blank equals cell fraction numerator square root of 1 minus q squared end root over denominator q end fraction end cell end table$

$table attributes columnalign right center left columnspacing 0px end attributes row cell sec space straight beta end cell equals cell fraction numerator 1 over denominator cos space straight beta end fraction end cell row blank equals cell 1 over straight q end cell end table$

$table attributes columnalign right center left columnspacing 0px end attributes row cell cosec space straight beta end cell equals cell fraction numerator 1 over denominator sin space straight beta end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 1 minus straight q squared end root end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 1 minus straight q squared end root end fraction cross times fraction numerator square root of 1 minus straight q squared end root over denominator square root of 1 minus straight q squared end root end fraction end cell row blank equals cell fraction numerator square root of 1 minus straight q squared end root over denominator 1 minus straight q squared end fraction end cell end table$

$table attributes columnalign right center left columnspacing 0px end attributes row cell cot space straight beta end cell equals cell fraction numerator 1 over denominator tan space straight beta end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style fraction numerator square root of 1 minus straight q squared end root over denominator straight q end fraction end style end fraction end cell row blank equals cell fraction numerator straight q over denominator square root of 1 minus straight q squared end root end fraction end cell row blank equals cell fraction numerator straight q over denominator square root of 1 minus straight q squared end root end fraction cross times fraction numerator square root of 1 minus straight q squared end root over denominator square root of 1 minus straight q squared end root end fraction end cell row blank equals cell fraction numerator straight q square root of 1 minus straight q squared end root over denominator 1 minus straight q squared end fraction end cell end table$

Dengan demikian, perbandingan trigonometri yang lain yaitu sin space beta equals square root of 1 minus q squared end root , $tan space beta equals fraction numerator square root of 1 minus q squared end root over denominator q end fraction$ , sec space beta equals 1 over q , $cosec space beta equals fraction numerator square root of 1 minus q squared end root over denominator 1 minus q squared end fraction$ , dan $c o t space beta equals fraction numerator q square root of 1 minus q squared end root over denominator square root of 1 minus q squared end root end fraction$ .