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Jika α∘ sudut lancip, tentukan perbandingan trigonometri sudut  yang lain, untuk: b) cos α∘=75​

Pertanyaan

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

b) cos space alpha degree equals 5 over 7 

F. Faiz

Master Teacher

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Pembahasan

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

cos space alpha degree equals samping over miring

Sehingga, pada soal diketahui nilai sisi samping alpha degree adalah 5 dan nilai sisi miring alpha degree adalah 7.

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

table attributes columnalign right center left columnspacing 0px end attributes row cell depan squared end cell equals cell miring squared minus samping squared end cell row depan equals cell plus-or-minus square root of miring squared minus samping squared end root end cell row blank equals cell plus-or-minus square root of 7 squared minus 5 squared end root end cell row blank equals cell plus-or-minus square root of 49 minus 25 end root end cell row blank equals cell plus-or-minus square root of 24 end cell row blank equals cell plus-or-minus 2 square root of 6 end cell row blank equals cell 2 square root of 6 end cell end table

Nilai sisi samping alpha degree adalah 2 square root of 6.

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 cos space alpha end cell equals cell 5 over 7 end cell row blank blank blank row cell sin space alpha end cell equals cell fraction numerator 2 square root of 6 over denominator 7 end fraction end cell row blank blank blank row cell tan space alpha end cell equals cell fraction numerator 2 square root of 6 over denominator 5 end fraction 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 fraction numerator 2 square root of 6 over denominator 7 end fraction end style end fraction end cell row blank equals cell fraction numerator 7 over denominator 2 square root of 6 end fraction cross times fraction numerator square root of 6 over denominator square root of 6 end fraction end cell row blank equals cell 7 over 12 square root of 6 end cell 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 5 over 7 end style end fraction end cell row blank equals cell 7 over 5 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 2 square root of 6 over denominator 5 end fraction end style end fraction end cell row blank equals cell fraction numerator 5 over denominator 2 square root of 6 end fraction cross times fraction numerator square root of 6 over denominator square root of 6 end fraction end cell row blank equals cell 5 over 12 square root of 6 end cell end table

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