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Diket titik straight Q space equals left parenthesis 2 comma negative 3 right parenthesis space dan space less than XOQ equals space straight theta. Tentukan ke-6 perbandingan trigonometri yang lain

A. Rahmawati

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Pembahasan

Sisi miring OX dapat dicari dengan menggunakan teorema Pythagoras:

table attributes columnalign right center left columnspacing 0px end attributes row cell XQ ² space end cell equals cell space OQ ² space plus space OX ² space end cell row cell space XQ ² space end cell equals cell space minus 3 ² space plus space 2 ² space space end cell row cell XQ ² space end cell equals cell space 9 space plus 4 space space end cell row cell XQ space end cell equals cell space square root of 13 end cell end table

Akan dicari nilai sin 

table attributes columnalign right center left columnspacing 0px end attributes row cell Sin space straight B space end cell equals cell fraction numerator space depan over denominator miring end fraction end cell row cell space space Sin space straight B space end cell equals cell space fraction numerator negative 3 over denominator square root of 13 end fraction space end cell row blank equals cell space fraction numerator negative 3 over denominator square root of 13 end fraction straight x fraction numerator square root of 13 over denominator square root of 13 end fraction end cell row blank equals cell fraction numerator negative 3 over denominator 13 end fraction square root of 13 space end cell row cell space Cos space straight B space end cell equals cell space samping over miring space space space end cell row cell Cos space straight B space end cell equals cell space fraction numerator 2 over denominator square root of 13 end fraction end cell row blank equals cell fraction numerator 2 over denominator square root of 13 end fraction straight x fraction numerator square root of 13 over denominator square root of 13 end fraction end cell row blank equals cell fraction numerator 2 square root of 13 over denominator 13 end fraction space space space end cell row cell Tan space straight B space end cell equals cell space depan over samping space end cell row cell space Tan space straight B space end cell equals cell space fraction numerator negative 3 over denominator 2 end fraction space space space end cell row cell Sec space straight B space end cell equals cell space kebalikan space cos space straight B space end cell row blank equals cell fraction numerator 1 over denominator fraction numerator 2 square root of 13 over denominator 13 end fraction end fraction end cell row blank equals cell fraction numerator 13 over denominator 2 square root of 13 end fraction straight x fraction numerator 2 square root of 13 over denominator 2 square root of 13 end fraction end cell row blank equals cell fraction numerator 2 square root of 13 over denominator 52 end fraction end cell row cell Cosec space straight B space end cell equals cell space kebalikan space sin space straight B end cell row blank equals cell fraction numerator 1 over denominator fraction numerator negative 3 over denominator 13 end fraction square root of 13 space end fraction end cell row blank equals cell fraction numerator 13 over denominator negative 3 square root of 13 end fraction straight x fraction numerator negative 3 square root of 13 over denominator negative 3 square root of 13 end fraction end cell row blank equals cell fraction numerator negative 39 square root of 13 over denominator 108 end fraction end cell row cell Cotan space straight B space end cell equals cell space kebalikan space tan space straight B end cell row blank equals cell fraction numerator 1 over denominator tan space straight B end fraction end cell row blank equals cell fraction numerator 1 over denominator fraction numerator negative 3 over denominator 2 end fraction end fraction space end cell row blank equals cell fraction numerator 2 over denominator negative 3 end fraction end cell end table

Jadi, ke-6 perbandingan trigonometri yang lain sin space straight B equals fraction numerator negative 3 over denominator 13 end fraction square root of 13 comma space cos space straight B equals fraction numerator 2 square root of 13 over denominator 13 end fraction comma space tan space straight B equals fraction numerator negative 3 over denominator 2 end fraction comma space coses space straight B equals fraction numerator negative 39 square root of 13 over denominator 108 end fraction comma sec equals fraction numerator 2 square root of 13 over denominator 52 end fraction comma space cotan equals fraction numerator 2 over denominator negative 3 end fraction

 

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