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Jika sin 11∘=p, maka sin 49∘=....

Pertanyaan

Jika begin mathsize 14px style sin space 11 degree equals p end style, maka begin mathsize 14px style sin space 49 degree equals end style....

  1. begin mathsize 14px style 1 half open parentheses square root of 3 plus 3 p squared end root minus p close parentheses end style 

  2. begin mathsize 14px style 1 half open parentheses square root of 1 plus p squared end root minus p square root of 3 close parentheses end style 

  3. begin mathsize 14px style 1 half open parentheses square root of 3 minus 3 p squared end root minus p close parentheses end style 

  4. begin mathsize 14px style 1 half open parentheses square root of 1 minus p squared end root minus p square root of 3 close parentheses end style 

  5. begin mathsize 14px style 1 half open parentheses square root of 1 minus p squared end root minus p close parentheses end style 

M. Robo

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Karena 49° = 60° - 11° , maka

sin 49° sin (60° - 11°)

Ingat bahwa

sin (B) sin cos -cos sin B

Sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin invisible function application 49 degree end cell equals cell sin invisible function application open parentheses 60 degree minus 11 degree close parentheses end cell row blank equals cell sin invisible function application 60 degree cos invisible function application 11 degree minus cos invisible function application 60 degree sin invisible function application 11 degree end cell row blank equals cell 1 half square root of 3 times cos invisible function application 11 degree minus 1 half times p end cell row blank blank blank end table end style 

Untuk mencari nilai dari cos11°  perhatikan segitiga berikut

Perhatikan bahwa sin 11° p . Karena begin mathsize 14px style sin invisible function application 11 degree equals fraction numerator B C over denominator A C end fraction end style, maka

begin mathsize 14px style fraction numerator B C over denominator A C end fraction equals p fraction numerator B C over denominator A C end fraction equals p over 1 end style 

Jika dimisalkan BC p , maka AC = 1

Panjang sisi AB dapat dicari menggunakan teorema Pythagoras, yaitu

begin mathsize 14px style A B equals square root of A C squared minus B C squared end root A B equals square root of 1 squared minus p squared end root A B equals square root of 1 minus p squared end root end style 

Sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos invisible function application 11 degree end cell equals cell fraction numerator A B over denominator A C end fraction end cell row blank equals cell fraction numerator square root of 1 minus p squared end root over denominator 1 end fraction end cell row blank equals cell square root of 1 minus p squared end root end cell end table end style 

Maka didapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin invisible function application 49 degree end cell equals cell 1 half square root of 3 times cos invisible function application 11 degree minus 1 half times p end cell row blank equals cell 1 half square root of 3 times square root of 1 minus p squared end root minus 1 half times p end cell row blank equals cell 1 half square root of 3 minus 3 p squared end root minus 1 half times p end cell row blank equals cell 1 half open parentheses square root of 3 minus 3 p squared end root minus p close parentheses end cell row blank blank blank end table end style 

Jadi, jawaban yang tepat adalah C.

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