Nilai dari tan 840∘ + tan 660∘ = ...

Pertanyaan

Nilai dari tan space 840 degree space plus space tan space 660 degree space equals space...space space 

  1. negative 2 square root of 3space space 

  2. negative square root of 3space space 

  3. 0space space 

  4. square root of 3space space 

  5. 2 square root of 3space space 

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

nilai dari tan space 840 degree space plus space tan space 660 degree adalah negative 2 square root of 3space space 

Pembahasan

Ingat,

Rumus Perbandingan Trigonometri untuk Penjumlahan Dua Sudut (Tangen)

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

Rumus Perbandingan Trigonometri untuk Selisih Dua Sudut (Tangen)

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

Sudut Berelasi (Sudut lebih besar 360 degree)

tan space open parentheses k times 360 degree plus A close parentheses equals tan space A

Sudut Berelasi (Kuadran II)

tan space open parentheses 180 degree minus A close parentheses equals negative tan space A

Berdasarkan rumus tersebut, diperoleh sebagai berikut

Menghitung nilai dari tan space 720 degree

tan space 720 degree equals tan space open parentheses 2 times 360 degree plus 0 degree close parentheses equals tan space 0 degree equals 0

Menghitung Nilai tan space 840 degree

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space 840 degree end cell equals cell tan space left parenthesis 720 degree plus 120 degree right parenthesis end cell row blank equals cell fraction numerator tan space 720 degree space plus space tan space 120 degree over denominator 1 minus tan space 720 degree space tan space 120 degree end fraction end cell row blank equals cell fraction numerator 0 plus open parentheses tan space open parentheses 180 degree minus 60 degree close parentheses close parentheses over denominator 1 minus 0 end fraction end cell row blank equals cell fraction numerator 0 plus open parentheses negative space tan 60 degree close parentheses over denominator 1 minus 0 end fraction end cell row blank equals cell fraction numerator negative space tan 60 degree over denominator 1 end fraction end cell row blank equals cell negative space tan 60 degree end cell row blank equals cell negative square root of 3 end cell end table

Menghitung Nilai tan space 660 degree

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space 660 degree end cell equals cell tan space left parenthesis 720 degree minus 60 degree right parenthesis end cell row blank equals cell fraction numerator tan space 720 degree space minus space tan space 60 degree over denominator 1 plus tan space 720 degree space tan space 60 degree end fraction end cell row blank equals cell fraction numerator 0 minus space tan space 60 degree over denominator 1 minus 0 end fraction end cell row blank equals cell fraction numerator negative space tan space 60 degree over denominator 1 end fraction end cell row blank equals cell negative space tan space 60 degree end cell row blank equals cell negative square root of 3 end cell end table

Menghitung nilai dari tan space 840 degree space plus space tan space 660 degree

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space 840 degree space plus space tan space 660 degree space end cell equals cell space minus square root of 3 space plus space open parentheses negative square root of 3 close parentheses end cell row blank equals cell negative square root of 3 minus square root of 3 end cell row blank equals cell negative 2 square root of 3 end cell end table

Dengan demikian, nilai dari tan space 840 degree space plus space tan space 660 degree adalah negative 2 square root of 3space space 

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Pertanyaan serupa

A+B+C=π​⇒⇒​A+B=π−Ctan (A+B)=tan (π−C)​  Gunakan hubungan tersebut untuk memperoleh relasi: tan A+tan B+tan C=tan A tan B tan C  Lalu, jika tan A=2 dan tan B=34​, buktikan A=C.

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