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Pertanyaan

Hitung nilai dari setiap pernyataan trigonometri berikut.

c. fraction numerator cos space 45 degree over denominator sec space 30 degree plus csc space 30 degree end fraction 

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Pembahasan

Ingat kembali nilai-nilai trigonometri pada sudut istimewa berikut:

Nilai dari fraction numerator cos space 45 degree over denominator sec space 30 degree plus csc space 30 degree end fraction dapat ditentukan sebagai berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator cos space 45 degree over denominator sec space 30 degree plus csc space 30 degree end fraction end cell equals cell fraction numerator begin display style 1 half end style square root of 2 over denominator begin display style 2 over 3 end style square root of 3 plus 2 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator square root of 2 over denominator 2 end fraction end style over denominator begin display style fraction numerator 2 square root of 3 over denominator 3 end fraction end style plus 2 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator square root of 2 over denominator 2 end fraction end style over denominator begin display style fraction numerator 2 square root of 3 plus 6 over denominator 3 end fraction end style end fraction end cell row blank equals cell fraction numerator square root of 2 over denominator 2 end fraction cross times fraction numerator 3 over denominator 2 square root of 3 plus 6 end fraction end cell row blank equals cell fraction numerator 3 square root of 2 over denominator 4 square root of 3 plus 12 end fraction cross times fraction numerator 4 square root of 3 minus 12 over denominator 4 square root of 3 minus 12 end fraction end cell row blank equals cell fraction numerator 12 square root of 6 minus 36 square root of 2 over denominator 16 cross times 3 minus 144 end fraction end cell row blank equals cell fraction numerator 12 square root of 6 minus 36 square root of 2 over denominator 48 minus 144 end fraction end cell row blank equals cell fraction numerator 12 square root of 6 minus 36 square root of 2 over denominator negative 96 end fraction end cell end table   

Jadi, fraction numerator cos space 45 degree over denominator sec space 30 degree plus csc space 30 degree end fraction equals fraction numerator 12 square root of 6 minus 36 square root of 2 over denominator negative 96 end fraction.

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