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Jika dalam segitiga ABC diketahui 3 sin A + 4 cos B = 1 dan 3 cos A + 4 sin B = 6, maka sin C = ...

Jika dalam segitiga ABC diketahui 3 sin A + 4 cos B = 1 dan 3 cos A + 4 sin B = 6, maka sin C = ...

  1. begin mathsize 12px style 1 half end style

  2. size 12px 1 over size 12px 2 square root of size 12px 2

  3. size 12px 1 over size 12px 2 square root of size 12px 3

  4. square root of size 12px 3

  5. 1

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A. Acfreelance

Master Teacher

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3 sin A + 4 cos B = 1 ... (1) 3 cos A + 4 sin B = 6 ... (2) Persamaan (1) dan (2) di kuadratkan lalu di jumlahkan, maka: Ingat! maka: Sudut dalam segitiga ABC, maka C = 180 - (A + B) Sehingga, nilai dari sin C yaitu:

3 sin A + 4 cos B = 1 ... (1)

3 cos A + 4 sin B = 6 ... (2)

Persamaan (1) dan (2) di kuadratkan lalu di jumlahkan, maka:

begin mathsize 12px style open parentheses 3 space sin space A plus 4 space cos space B equals 1 close parentheses squared left right arrow 9 space sin squared space A plus space 16 space cos squared space B plus 24 space sin space A space cos space B equals 1 open parentheses 3 space cos space A plus 4 space sin space B equals 6 close parentheses squared left right arrow 9 space cos squared space A plus 16 space sin squared space B plus 24 space cos space A space sin space B space equals space 36 9 space sin squared space A plus space 16 space cos squared space B plus 24 space sin space A space cos space B equals 1 bottom enclose 9 space cos squared space A plus 16 space sin squared space B plus 24 space cos space A space sin space B space equals space 36 end enclose space plus 9 open parentheses sin squared space A plus cos squared space A close parentheses plus 16 open parentheses sin squared space B plus cos squared space B close parentheses plus 24 open parentheses sin space A space cos space B plus cos space A space sin space B close parentheses equals 37 end style

 

Ingat!

size 12px sin to the power of size 12px 2 size 12px space size 12px A size 12px plus size 12px cos to the power of size 12px 2 size 12px space size 12px A size 12px equals size 12px 1 size 12px sin size 12px space open parentheses size 12px A size 12px plus size 12px B close parentheses size 12px equals size 12px sin size 12px space size 12px A size 12px space size 12px cos size 12px space size 12px B size 12px plus size 12px space size 12px cos size 12px space size 12px A size 12px space size 12px sin size 12px space size 12px B size 12px sin size 12px space open parentheses size 12px A size 12px minus size 12px B close parentheses size 12px equals size 12px sin size 12px space size 12px A size 12px space size 12px cos size 12px space size 12px B size 12px minus size 12px space size 12px cos size 12px space size 12px A size 12px space size 12px sin size 12px space size 12px B

maka:

size 12px 9 open parentheses size 12px sin to the power of size 12px 2 size 12px space size 12px A size 12px plus size 12px cos to the power of size 12px 2 size 12px space size 12px A close parentheses size 12px plus size 12px 16 open parentheses size 12px sin to the power of size 12px 2 size 12px space size 12px B size 12px plus size 12px cos to the power of size 12px 2 size 12px space size 12px B close parentheses size 12px plus size 12px 24 open parentheses size 12px sin size 12px space size 12px A size 12px space size 12px cos size 12px space size 12px B size 12px plus size 12px cos size 12px space size 12px A size 12px space size 12px sin size 12px space size 12px B close parentheses size 12px equals size 12px 37 size 12px 9 size 12px. size 12px 1 size 12px plus size 12px 16 size 12px. size 12px 1 size 12px plus size 12px 24 open parentheses size 12px sin open parentheses size 12px A size 12px plus size 12px B close parentheses close parentheses size 12px equals size 12px 37 size 12px 24 open parentheses size 12px sin open parentheses size 12px A size 12px plus size 12px B close parentheses close parentheses size 12px equals size 12px 12 size 12px sin open parentheses size 12px A size 12px plus size 12px B close parentheses size 12px equals size 12px 1 over size 12px 2

Sudut dalam segitiga ABC, maka C = 180begin mathsize 12px style degree end style - (A + B)

Sehingga, nilai dari sin C yaitu:

size 12px sin size 12px space size 12px C size 12px equals size 12px sin size 12px space open parentheses size 12px 180 size 12px degree size 12px minus open parentheses size 12px A size 12px plus size 12px B close parentheses close parentheses size 12px sin size 12px space size 12px C size 12px equals size 12px sin size 12px space size 12px 180 size 12px degree size 12px space size 12px cos open parentheses size 12px A size 12px plus size 12px B close parentheses size 12px minus size 12px cos size 12px space size 12px 180 size 12px degree size 12px space size 12px sin open parentheses size 12px A size 12px plus size 12px B close parentheses size 12px sin size 12px space size 12px C size 12px equals size 12px sin size 12px space open parentheses size 12px A size 12px plus size 12px B close parentheses size 12px sin size 12px space size 12px C size 12px equals size 12px 1 over size 12px 2

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