Jika diketahui cos β=25−24​, buatlah perbandingan trigonometri lengkap (sin, cos, tg, sec, cosec, ctg)!

Pertanyaan

Jika diketahui begin mathsize 14px style cos space beta equals fraction numerator negative 24 over denominator 25 end fraction end style, buatlah perbandingan trigonometri lengkap (sin, cos, tg, sec, cosec, ctg)!

A. Acfreelance

Master Teacher

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Jawaban

nilai perbandingan trigonometri lengkap (sin, cos, tg, sec, cosec, ctg) berturut-turut adalah begin mathsize 14px style plus-or-minus 7 over 25 end stylebegin mathsize 14px style negative 24 over 25 end stylebegin mathsize 14px style plus-or-minus 7 over 24 end stylebegin mathsize 14px style negative 25 over 24 end stylebegin mathsize 14px style plus-or-minus 25 over 7 end style, dan begin mathsize 14px style plus-or-minus 24 over 7 end style.

Pembahasan

Diketahui begin mathsize 14px style cos space beta equals fraction numerator negative 24 over denominator 25 end fraction end style, maka diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row x equals cell negative 24 end cell row r equals 25 row cell y squared end cell equals cell r squared minus x squared end cell row blank equals cell 25 squared minus open parentheses negative 24 close parentheses squared end cell row blank equals cell 625 minus 576 end cell row blank equals 49 row y equals cell plus-or-minus square root of 49 end cell row blank equals cell plus-or-minus 7 end cell end table end style 

Dengan menerapkan konsep perbandingan trigonometri, diperoleh perhitungan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin space beta end cell equals cell y over r end cell row blank equals cell fraction numerator plus-or-minus 7 over denominator 25 end fraction end cell row blank equals cell plus-or-minus 7 over 25 end cell row cell cos space beta end cell equals cell x over r end cell row blank equals cell fraction numerator negative 24 over denominator 25 end fraction end cell row blank equals cell negative 24 over 25 end cell row cell tg space beta end cell equals cell y over x end cell row blank equals cell fraction numerator plus-or-minus 7 over denominator negative 24 end fraction end cell row blank equals cell plus-or-minus 7 over 24 end cell row cell sec space beta end cell equals cell r over x end cell row blank equals cell fraction numerator 25 over denominator negative 24 end fraction end cell row blank equals cell negative 25 over 24 end cell row cell cosec space beta end cell equals cell r over y end cell row blank equals cell fraction numerator 25 over denominator plus-or-minus 7 end fraction end cell row blank equals cell plus-or-minus 25 over 7 end cell row cell ctg space beta end cell equals cell x over y end cell row blank equals cell fraction numerator negative 24 over denominator plus-or-minus 7 end fraction end cell row blank equals cell plus-or-minus 24 over 7 end cell end table end style 

Jadi, nilai perbandingan trigonometri lengkap (sin, cos, tg, sec, cosec, ctg) berturut-turut adalah begin mathsize 14px style plus-or-minus 7 over 25 end stylebegin mathsize 14px style negative 24 over 25 end stylebegin mathsize 14px style plus-or-minus 7 over 24 end stylebegin mathsize 14px style negative 25 over 24 end stylebegin mathsize 14px style plus-or-minus 25 over 7 end style, dan begin mathsize 14px style plus-or-minus 24 over 7 end style.

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