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Pertanyaan

Tentukan perbandingan trigonometri begin mathsize 14px style sin space beta end stylebegin mathsize 14px style cos space beta end stylebegin mathsize 14px style tan space beta end stylebegin mathsize 14px style cosec space beta end stylebegin mathsize 14px style secan space beta end style dan begin mathsize 14px style cotan space beta end style pada segitiga berikut.


F. Nur

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Pembahasan

Menentukan panjang AC dengan Teorema Pythagoras.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row AC equals cell square root of AB squared plus BC squared end root end cell row blank equals cell square root of 4 squared plus 3 cubed end root end cell row blank equals cell square root of 16 plus 9 end root end cell row blank equals cell square root of 25 end cell row blank equals 5 end table end style 

Perbandingan trigonometri:

begin mathsize 14px style sin space beta equals AB over AC equals 4 over 5 cos space beta equals BC over AC equals 3 over 5 tan space beta equals AB over BC equals 4 over 3 cosec space beta equals fraction numerator 1 over denominator sin space beta end fraction equals 5 over 4 secan space beta equals fraction numerator 1 over denominator cos space beta end fraction equals 5 over 3 cotan space beta equals fraction numerator 1 over denominator tan space beta end fraction equals 3 over 4 end style  

Jadi, perbandingan trigonometri pada segitiga tersebut adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank beta end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 4 over 5 end cell end table end stylebegin mathsize 14px style cos table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank beta end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 3 over 5 end cell end table end stylebegin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank tan end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank beta end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 4 over 3 end cell end table end stylebegin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cosec end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank beta end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 5 over 4 end cell end table end stylebegin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank secan end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank beta end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 5 over 3 end cell end table end style dan begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cotan end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank beta end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 3 over 4 end cell end table end style.

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Tentukan nilai perbandingan trigonometri pada setiap segitiga berikut untuk A.

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