Nilai dari tan 255∘ adalah ....

Pertanyaan

Nilai dari $\tan\;255^\circ$ adalah ....

S. Difhayanti

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. Dr. Hamka

Jawaban terverifikasi

Jawaban

nilai dari tan space 255 degree

adalah

table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 3 end cell end table

Pembahasan

Dengan menggunakan rumus jumlah sudut trigonometri pada tangen. Rumus jumlah dan selisih sudut pada trigonometri adalah

$tan space left parenthesis straight A plus straight B right parenthesis equals fraction numerator tan space straight A plus tan space straight B over denominator 1 minus tan space straight A space tan space straight B end fraction$

Sehingga diperoleh,

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan space 255 degree end cell equals cell tan space left parenthesis 180 degree plus 75 degree right parenthesis end cell row blank equals cell fraction numerator tan space 180 degree plus tan space 75 degree over denominator 1 minus tan space 180 degree space tan space 75 degree space end fraction end cell row blank equals cell fraction numerator 0 plus tan space 75 degree over denominator 1 minus 0 cross times tan space 75 degree end fraction end cell row blank equals cell fraction numerator tan space 75 degree over denominator 1 end fraction end cell end table$

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan space 75 degree end cell equals cell tan space open parentheses 45 degree plus 30 degree close parentheses end cell row blank equals cell fraction numerator tan space 45 degree plus tan space 30 degree over denominator 1 minus tan space 45 degree tan space 30 degree end fraction end cell row blank equals cell fraction numerator 1 plus begin display style 1 third end style square root of 3 over denominator 1 minus 1 cross times begin display style 1 third end style square root of 3 end fraction end cell row blank equals cell fraction numerator 1 plus begin display style 1 third end style square root of 3 over denominator 1 minus begin display style 1 third end style square root of 3 end fraction cross times fraction numerator square root of 3 over denominator square root of 3 end fraction end cell row blank equals cell fraction numerator square root of 3 plus 1 over denominator square root of 3 minus 1 end fraction end cell row blank equals cell fraction numerator square root of 3 plus 1 over denominator square root of 3 minus 1 end fraction cross times fraction numerator square root of 3 plus 1 over denominator square root of 3 plus 1 end fraction end cell row blank equals cell fraction numerator 3 plus 2 square root of 3 plus 1 over denominator 3 minus 1 end fraction end cell row blank equals cell fraction numerator 4 plus 2 square root of 3 over denominator 2 end fraction end cell row blank equals cell 2 plus square root of 3 end cell end table$

Jadi, nilai dari tan space 255 degree adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 3 end cell end table .

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