Hitunglah tan (A+B) dan tan (A−B) jika : c. sin A=0,6 dan sin B=0,4 dengan A dan B sudut tumpul.

Pertanyaan

Hitunglah tan space left parenthesis A plus B right parenthesis space dan space tan space left parenthesis A minus B right parenthesis jika :

c. sin space A equals 0 comma 6 space dan space sin space B equals 0 comma 4 dengan A space dan space B sudut tumpul.

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

diperoleh table attributes columnalign right center left columnspacing 0px end attributes row cell tan space left parenthesis A plus B right parenthesis end cell equals cell fraction numerator negative 3 square root of 21 minus 8 over denominator 4 square root of 21 minus 6 end fraction space dan space tan space left parenthesis A minus B right parenthesis equals fraction numerator negative 3 square root of 21 plus 8 over denominator 4 square root of 21 plus 6 end fraction end cell end table.

Pembahasan

Pertama, ingat :

sin space A equals depan over miring equals 0 comma 6 equals 6 over 10 equals 3 over 5 sin space B equals depan over miring equals 0 comma 4 equals 4 over 10 equals 2 over 5

Dengan segitiga siku-siku,

Karena A space dan space B sudut tumpul, maka tangen di kuadran II bernilai negatif, sehingga:

tan space A equals depan over samping equals negative 3 over 4 tan space B equals depan over samping equals negative fraction numerator 2 over denominator square root of 21 end fraction

Dengan rumus jumlah dan selisih dua sudut pada tangen :

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space left parenthesis A plus B right parenthesis end cell equals cell fraction numerator tan space A plus tan space B over denominator 1 minus tan space A space tan space B end fraction end cell row blank equals cell fraction numerator negative 3 over 4 plus open parentheses negative fraction numerator 2 over denominator square root of 21 end fraction close parentheses over denominator 1 minus open parentheses negative 3 over 4 close parentheses times open parentheses negative fraction numerator 2 over denominator square root of 21 end fraction close parentheses end fraction end cell row blank equals cell fraction numerator fraction numerator negative 3 square root of 21 minus 8 over denominator 4 square root of 21 end fraction over denominator fraction numerator 4 square root of 21 minus 6 over denominator 4 square root of 21 end fraction end fraction end cell row blank equals cell fraction numerator negative 3 square root of 21 minus 8 over denominator 4 square root of 21 minus 6 end fraction end cell row cell tan space left parenthesis A minus B right parenthesis end cell equals cell fraction numerator tan space A minus tan space B over denominator 1 plus tan space A space tan space B end fraction end cell row blank equals cell fraction numerator negative 3 over 4 minus open parentheses negative fraction numerator 2 over denominator square root of 21 end fraction close parentheses over denominator 1 plus open parentheses negative 3 over 4 close parentheses times open parentheses negative fraction numerator 2 over denominator square root of 21 end fraction close parentheses end fraction end cell row blank equals cell fraction numerator fraction numerator negative 3 square root of 21 plus 8 over denominator 4 square root of 21 end fraction over denominator fraction numerator 4 square root of 21 plus 6 over denominator 4 square root of 21 end fraction end fraction end cell row blank equals cell fraction numerator negative 3 square root of 21 plus 8 over denominator 4 square root of 21 plus 6 end fraction end cell end table

Jadi, diperoleh table attributes columnalign right center left columnspacing 0px end attributes row cell tan space left parenthesis A plus B right parenthesis end cell equals cell fraction numerator negative 3 square root of 21 minus 8 over denominator 4 square root of 21 minus 6 end fraction space dan space tan space left parenthesis A minus B right parenthesis equals fraction numerator negative 3 square root of 21 plus 8 over denominator 4 square root of 21 plus 6 end fraction end cell end table.

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Hitunglah tan (A+B) dan tan (A−B) jika : a. sin A=54​, cos B=135​ dengan A dan B sudut lancip.

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