Pertanyaan

Jika α ∘ sudut lancip, tentukan perbandingan trigonometri sudut yang lain, untuk: a) sin α ∘ = 3 1 ​

Jika  sudut lancip, tentukan perbandingan trigonometri sudut alpha degree yang lain, untuk:

a) 

F. Faiz

Master Teacher

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Pembahasan

Ingatlah pada perbandingan sisi (trigonometri) segitiga siku-siku. Sehingga, pada soal diketahui nilai sisi depan adalah dan nilai sisi miring adalah . Kemudian tentukan terlebih dahulu nilai sisi samping dengan menggunakan Pythagoras. Nilai sisi samping adalah . Kemudian ingatlah perbandingan-perbandingan trigonometri, yaitu: Maka, perbandingan trigonometri sudut yang lain, yaitu:

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

sin space alpha degree equals depan over miring

Sehingga, pada soal diketahui nilai sisi depan alpha degree adalah 1 dan nilai sisi miring alpha degree adalah 3.

Kemudian tentukan terlebih dahulu nilai sisi samping alpha degree dengan menggunakan Pythagoras.

table attributes columnalign right center left columnspacing 0px end attributes row cell samping squared end cell equals cell miring squared minus depan squared end cell row samping equals cell plus-or-minus square root of miring squared minus depan squared end root end cell row blank equals cell plus-or-minus square root of 3 squared minus 1 squared end root end cell row blank equals cell plus-or-minus square root of 9 minus 1 end root end cell row blank equals cell plus-or-minus square root of 8 end cell row blank equals cell plus-or-minus 2 square root of 2 end cell row blank equals cell 2 square root of 2 end cell end table

Nilai sisi samping alpha degree adalah 2 square root of 2.

Kemudian ingatlah perbandingan-perbandingan trigonometri, yaitu:

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

Maka, perbandingan trigonometri sudut alpha degree yang lain, yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space alpha end cell equals cell 1 third end cell row blank blank blank row cell cos space alpha end cell equals cell fraction numerator 2 square root of 2 over denominator 3 end fraction end cell row blank blank blank row cell tan space alpha end cell equals cell fraction numerator 1 over denominator 2 square root of 2 end fraction end cell row blank equals cell fraction numerator 1 over denominator 2 square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row blank equals cell 1 fourth square root of 2 end cell row blank blank blank row cell csc space alpha end cell equals cell fraction numerator 1 over denominator sin space alpha end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style 1 third end style end fraction end cell row blank equals 3 row blank blank blank row cell sec space alpha end cell equals cell fraction numerator 1 over denominator cos space alpha end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style fraction numerator 2 square root of 2 over denominator 3 end fraction end style end fraction end cell row blank equals cell fraction numerator 3 over denominator 2 square root of 2 end fraction end cell row blank equals cell fraction numerator 3 over denominator 2 square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row blank equals cell 3 over 4 square root of 2 end cell row blank blank blank row cell cot space alpha end cell equals cell fraction numerator 1 over denominator tan space alpha end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style fraction numerator square root of 2 over denominator 4 end fraction end style end fraction end cell row blank equals cell fraction numerator 4 over denominator square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row blank equals cell 4 over 2 square root of 2 end cell row blank equals cell 2 square root of 2 end cell end table

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