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Tentukan nilai dari: sin 3 5 ∘ cos 5 ∘ − cos 3 5 ∘ cos 8 5 ∘ .

Tentukan nilai dari: .

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S. Nur

Master Teacher

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diperoleh nilai .

diperoleh nilai sin space 35 degree space cos space 5 degree minus cos space 35 degree space cos space 85 degree equals 1 half.

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Pembahasan

Gunakan konsep rumus perkalian trigonometri dan sudut relasi . Ingat kembali nilai trigonometri sudut istimewa dan sudut istimewa di kuadran II . Perhatikan perhitungan berikut. Jadi, diperoleh nilai .

Gunakan konsep rumus perkalian trigonometri dan sudut relasi open parentheses 90 degree minus x close parentheses.

table attributes columnalign right center left columnspacing 2px end attributes row cell 2 space sin space straight A space cos space straight B end cell equals cell sin space open parentheses straight A plus straight B close parentheses plus sin space open parentheses straight A minus straight B close parentheses end cell row atau blank blank row cell sin space straight A space cos space straight B end cell equals cell 1 half open parentheses sin space open parentheses straight A plus straight B close parentheses plus sin space open parentheses straight A minus straight B close parentheses close parentheses end cell row blank blank blank row cell 2 space cos space straight A space cos space straight B end cell equals cell cos space open parentheses straight A plus straight B close parentheses plus cos space open parentheses straight A minus straight B close parentheses end cell row atau blank blank row cell cos space straight A space cos space straight B end cell equals cell 1 half open parentheses cos space open parentheses straight A plus straight B close parentheses plus cos space open parentheses straight A minus straight B close parentheses close parentheses end cell row blank blank blank row cell sin space open parentheses 90 degree minus alpha close parentheses end cell equals cell cos space alpha end cell row cell cos space open parentheses negative alpha close parentheses end cell equals cell cos space alpha end cell end table

Ingat kembali nilai trigonometri sudut istimewa 30 degree dan sudut istimewa di kuadran II 120 degree.

table attributes columnalign right center left columnspacing 2px end attributes row cell sin space 30 degree end cell equals cell 1 half end cell row cell cos space 120 degree end cell equals cell negative 1 half end cell end table

Perhatikan perhitungan berikut.

table attributes columnalign right center left columnspacing 2px end attributes row blank blank cell sin space 35 degree space cos space 5 degree minus cos space 35 degree space cos space 85 degree end cell row blank equals cell 1 half open parentheses sin space open parentheses 35 degree plus 5 degree close parentheses plus sin space open parentheses 35 degree minus 5 degree close parentheses close parentheses minus end cell row blank blank cell 1 half open parentheses cos space open parentheses 35 degree plus 85 degree close parentheses plus cos space open parentheses 35 degree minus 85 degree close parentheses close parentheses end cell row blank equals cell 1 half open parentheses sin space 40 degree plus sin space 30 degree close parentheses minus 1 half open parentheses cos space 120 degree plus cos space open parentheses negative 50 degree close parentheses close parentheses end cell row blank equals cell 1 half open parentheses sin space open parentheses 90 degree minus 50 degree close parentheses plus 1 half close parentheses minus 1 half open parentheses negative 1 half plus cos space 50 degree close parentheses end cell row blank equals cell 1 half open parentheses cos space 50 degree plus 1 half close parentheses minus 1 half open parentheses negative 1 half plus cos space 50 degree close parentheses end cell row blank equals cell fraction numerator cos space 50 degree over denominator 2 end fraction plus 1 fourth plus 1 fourth minus fraction numerator cos space 50 degree over denominator 2 end fraction end cell row blank equals cell open parentheses 1 fourth plus 1 fourth close parentheses plus open parentheses fraction numerator cos space 50 degree over denominator 2 end fraction minus fraction numerator cos space 50 degree over denominator 2 end fraction close parentheses end cell row blank equals cell 2 over 4 plus 0 end cell row blank equals cell 1 half end cell end table 

Jadi, diperoleh nilai sin space 35 degree space cos space 5 degree minus cos space 35 degree space cos space 85 degree equals 1 half.

Latihan Bab

Konsep Kilat

Jumlah dan Selisih Dua Sudut

Sudut Rangkap dan Sudut Paruh

Perkalian Trigonometri

407

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