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Diketahui: gambar Tentukan nilai sin α , cos α , tan α , secan α , cotan α .

Diketahui:


gambar


Tentukan nilai .

  1. ...space 

  2. ...space 

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S. Yoga

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

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Pembahasan

Mencari sisi AB: Karena suatu panjang tidak munfkin negatif, sehingga AB adalah 6. Dengan perbandingan sisi depan, sisi miring dan sisi samping terhadap suatu sudut pada segitiga siku-siku, didapat: Jadi,

Mencari sisi AB:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell AB squared end cell equals cell AC squared minus BC squared end cell row blank equals cell 10 squared minus 8 squared end cell row blank equals cell 100 minus 64 end cell row AB equals cell plus-or-minus square root of 36 end cell row blank equals cell plus-or-minus 6 end cell end table end style

Karena suatu panjang tidak munfkin negatif, sehingga AB adalah 6.
Dengan perbandingan sisi depan, sisi miring dan sisi samping terhadap suatu sudut pada segitiga siku-siku, didapat:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin space straight alpha end cell equals cell fraction numerator sisi space depan over denominator sisi space miring end fraction equals BC over AC equals 8 over 10 equals 4 over 5 end cell row cell cos space straight alpha end cell equals cell fraction numerator sisi space samping over denominator sisi space miring end fraction equals AB over AC equals 6 over 10 equals 3 over 5 end cell row cell tan space straight alpha end cell equals cell fraction numerator sisi space depan over denominator sisi space samping end fraction equals BC over AB equals 8 over 6 equals 4 over 3 end cell row cell secan space straight alpha end cell equals cell fraction numerator sisi space miring over denominator sisi space samping end fraction equals AC over AB equals 10 over 6 equals 5 over 3 end cell row cell cotan space straight alpha end cell equals cell fraction numerator sisi space samping over denominator sisi space depan end fraction equals AB over BC equals 6 over 8 equals 3 over 4 end cell end table end style 

Jadi, 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 straight alpha 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 table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma 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 cos 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 straight alpha 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 table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma 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 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 straight alpha 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 table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table 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 straight alpha 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 table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma 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 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 straight alpha 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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