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Diketahui segitiga ABC berikut: gambar Tentuka...

Diketahui segitiga ABC berikut:


gambar


Tentukan nilai begin mathsize 14px style sin space straight alpha comma space cos space straight alpha comma space tan space straight alpha comma space secan space straight alpha comma space cotan space straight alpha end style.

  1. ...space 

  2. ...space 

Jawaban:

Mencari sisi BC:

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

Karena suaru panjang tidak mungkin negatif, sehingga sisi BC adalah 4.
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 AB over AC equals 3 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 BC over AC equals 4 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 AB over BC equals 3 over 4 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 BC equals 5 over 4 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 BC over AB equals 4 over 3 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 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 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 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 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 cell 3 over 4 end cell end table s table attributes columnalign right center left columnspacing 0px end attributes row blank blank ecan 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 4 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 4 over 3 end cell end table end style 

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