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Tentukan nilai sin α, cos α, tan α, csc α, sec α, dan cot α pada segitiga berikut.

Pertanyaan

Tentukan nilai sin space alphacos space alphatan space alphacsc space alphasec space alpha, dan cot space alpha pada segitiga berikut.

F. Faiz

Master Teacher

Jawaban terverifikasi

Pembahasan

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

table attributes columnalign right center left columnspacing 0px end attributes row cell miring squared end cell equals cell tegak subscript 1 squared plus tegak subscript 2 squared end cell row miring equals cell plus-or-minus square root of tegak subscript 1 squared plus tegak subscript 2 squared end root end cell row blank equals cell plus-or-minus square root of 12 squared plus 5 squared end root end cell row blank equals cell plus-or-minus square root of 144 plus 25 end root end cell row blank equals cell plus-or-minus square root of 169 end cell row blank equals cell plus-or-minus 13 end cell row blank equals 13 end table

Panjang sisi miring adalah 13.

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 segitiga yaitu:

table row cell sin space straight alpha end cell equals cell 12 over 13 end cell space space space space row space space space space space space space row cell cos space straight alpha end cell equals cell 5 over 13 end cell space space space space row space space space space space space space row cell tan space straight alpha end cell equals cell 12 over 5 end cell space space space space row space space space 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 fraction numerator 1 over denominator begin display style 12 over 13 end style end fraction end cell equals cell 13 over 12 end cell row space space space space space 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 fraction numerator 1 over denominator begin display style 5 over 13 end style end fraction end cell equals cell 13 over 5 end cell row space space space space space 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 fraction numerator 1 over denominator begin display style 12 over 5 end style end fraction end cell equals cell 5 over 12 end cell end table

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Pertanyaan serupa

Tentukan nilai-nilai perbandingan trigonometri sudut α pada tiap gambar berikut: b.

207

5.0

Jawaban terverifikasi

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