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Pertanyaan

Tentukan nilai-nilai perbandingan trigonometri sudut alpha pada tiap gambar berikut:

b.

F. Faiz

Master Teacher

Jawaban terverifikasi

Pembahasan

Asumsikan sudut alpha terletak pada salah satu sudut pada segitiga.

Tentukan terlebih dahulu panjang sisi tegak lainnya pada segitiga siku-siku dengan menggunakan Teorema Pythagoras.

table attributes columnalign right center left columnspacing 0px end attributes row cell tegak subscript 1 squared end cell equals cell miring squared minus tegak subscript 2 squared end cell row cell tegak subscript 1 end cell equals cell plus-or-minus square root of miring squared minus tega straight k subscript 2 squared end root end cell row blank equals cell plus-or-minus square root of open parentheses 2 square root of 5 close parentheses squared minus 2 squared end root end cell row blank equals cell plus-or-minus square root of 20 minus 4 end root end cell row blank equals cell plus-or-minus square root of 16 end cell row blank equals cell plus-or-minus 4 end cell row blank equals 4 end table

Panjang sisi tegak di depan sudut alpha adalah 4.

Ingatlah perbandingan sisi (trigonometri) pada segitiga siku-siku.

table row cell sin space straight alpha end cell equals cell depan over miring end cell space space space space row cell cos space straight alpha end cell equals cell samping over miring end cell space space space space row cell tan space straight alpha end cell equals cell depan over samping end cell space space space space row cell csc space straight alpha end cell equals cell fraction numerator 1 over denominator sin space straight alpha end fraction end cell equals cell miring over depan end cell space space row cell sec space straight alpha end cell equals cell fraction numerator 1 over denominator cos space straight alpha end fraction end cell equals cell miring over samping end cell space space row cell cot space straight alpha end cell equals cell fraction numerator 1 over denominator tan space straight alpha end fraction end cell equals cell samping over depan end cell space space end table

Sehingga diperoleh nilai-nilai perbandingan trigonometri sudut alpha pada gambar yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space straight alpha end cell equals cell fraction numerator 4 over denominator 2 square root of 5 end fraction end cell row blank equals cell fraction numerator 4 over denominator 2 square root of 5 end fraction cross times fraction numerator square root of 5 over denominator square root of 5 end fraction end cell row blank equals cell fraction numerator 4 square root of 5 over denominator 2 times 5 end fraction end cell row blank equals cell 2 over 5 square root of 5 end cell row blank blank blank row cell cos space straight alpha end cell equals cell fraction numerator 2 over denominator 2 square root of 5 end fraction end cell row blank equals cell fraction numerator 2 over denominator 2 square root of 5 end fraction cross times fraction numerator square root of 5 over denominator square root of 5 end fraction end cell row blank equals cell fraction numerator 2 square root of 5 over denominator 2 times 5 end fraction end cell row blank equals cell 1 fifth square root of 5 end cell row blank blank blank row cell tan space straight alpha end cell equals cell 4 over 2 end cell row blank equals 2 row blank blank blank row cell csc space straight alpha end cell equals cell fraction numerator 1 over denominator sin space straight alpha end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style 2 over 5 end style square root of 5 end fraction end cell row blank equals cell fraction numerator 5 over denominator 2 square root of 5 end fraction cross times fraction numerator square root of 5 over denominator square root of 5 end fraction end cell row blank equals cell fraction numerator 5 square root of 5 over denominator 2 times 5 end fraction end cell row blank equals cell 1 half square root of 5 end cell row blank blank blank row cell sec space straight alpha end cell equals cell fraction numerator 1 over denominator begin display style 1 fifth end style square root of 5 end fraction end cell row blank equals cell fraction numerator 5 over denominator square root of 5 end fraction cross times fraction numerator square root of 5 over denominator square root of 5 end fraction end cell row blank equals cell 5 over 5 square root of 5 end cell row blank equals cell square root of 5 end cell row blank blank blank row cell cot space straight alpha end cell equals cell 1 half end cell end table

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