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Tunjukkan bahwa: sin 1 0 ∘ sin 3 0 ∘ sin 5 0 ∘ sin 7 0 ∘ = 16 1 ​

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S. Solehuzain

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

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terbukti bahwa sin 1 0 ∘ sin 3 0 ∘ sin 5 0 ∘ sin 7 0 ∘ = 16 1 ​ .

terbukti bahwa .

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Ingat rumus perkalian trigonometri 2 sin α sin β = cos ( α − β ) − cos ( α + β ) . Sehingga diperoleh ​ = = = = = = = ​ sin 1 0 ∘ sin 3 0 ∘ sin 5 0 ∘ sin 7 0 ∘ 2 1 ​ sin 1 0 ∘ sin 5 0 ∘ sin 7 0 ∘ 2 1 ​ . 2 1 ​ ( 2 sin 1 0 ∘ sin 5 0 ∘ ) 4 1 ​ ( cos ( 1 0 ∘ − 5 0 ∘ ) − cos ( 1 0 ∘ + 5 0 ∘ ) ) sin 7 0 ∘ 4 1 ​ ( cos ( − 4 0 ∘ ) − cos ( 6 0 ∘ ) ) sin 7 0 ∘ 4 1 ​ ( cos ( 4 0 ∘ ) − 2 1 ​ ) sin 7 0 ∘ ( 4 1 ​ cos ( 4 0 ∘ ) − 8 1 ​ ) sin 7 0 ∘ 4 1 ​ cos 4 0 ∘ sin 7 0 ∘ − 8 1 ​ sin 7 0 ∘ ​ ingat 2 cos α sin β = sin ( α + β ) − sin ( α − β ) Dengan demikian, terbukti bahwa sin 1 0 ∘ sin 3 0 ∘ sin 5 0 ∘ sin 7 0 ∘ = 16 1 ​ .

Ingat rumus perkalian trigonometri 
.

Sehingga diperoleh 

ingat 

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 fourth end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 40 degree end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 70 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank degree end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 over 8 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 70 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank degree end table equals 1 over 8 open parentheses 2 space cos table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 40 degree end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 70 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank degree end table close parentheses plus degree table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 over 8 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 70 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank degree end table equals 1 over 8 open parentheses sin open parentheses 40 degree plus 70 degree close parentheses minus sin open parentheses 40 degree minus 70 degree close parentheses close parentheses minus table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 over 8 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 70 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank degree end table equals 1 over 8 open parentheses sin open parentheses 110 degree close parentheses minus sin open parentheses negative 30 degree close parentheses close parentheses minus 1 over 8 table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 70 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank degree end table space text ingat end text space sin open parentheses negative a close parentheses equals negative sin open parentheses a close parentheses equals 1 over 8 open parentheses sin open parentheses 110 degree close parentheses minus open parentheses negative sin open parentheses 30 degree close parentheses close parentheses close parentheses minus 1 over 8 table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 70 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank degree end table equals 1 over 8 open parentheses sin open parentheses 110 degree close parentheses plus 1 half close parentheses minus 1 over 8 table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 70 end table degree equals 1 over 8 sin open parentheses 180 degree minus 70 degree close parentheses plus 1 over 16 minus 1 over 8 table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 70 end table degree equals 1 over 8 sin open parentheses 70 degree close parentheses plus 1 over 16 minus 1 over 8 table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 70 end table degree equals 1 over 16

Dengan demikian, terbukti bahwa .

Perdalam pemahamanmu bersama Master Teacher
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