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Hitung nilai berikut. sin(43π​)⋅sin(4π​)+cos(43π​)⋅cos(4π​)

Pertanyaan

Hitung nilai berikut.

begin mathsize 14px style sin open parentheses fraction numerator 3 straight pi over denominator 4 end fraction close parentheses times sin open parentheses straight pi over 4 close parentheses plus cos open parentheses fraction numerator 3 straight pi over denominator 4 end fraction close parentheses times cos open parentheses straight pi over 4 close parentheses end style 

H. Endah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta

Jawaban terverifikasi

Jawaban

nilai sin open parentheses fraction numerator 3 straight pi over denominator 4 end fraction close parentheses times sin open parentheses straight pi over 4 close parentheses plus cos open parentheses fraction numerator 3 straight pi over denominator 4 end fraction close parentheses times cos open parentheses straight pi over 4 close parentheses equals 0

Pembahasan

Ingat bahwa:

sin space open parentheses 180 minus straight A close parentheses equals sin space straight A cos space left parenthesis 180 minus straight A right parenthesis equals negative cos space straight A 

Sehingga penyelesaiannya adalah:

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell sin open parentheses fraction numerator 3 straight pi over denominator 4 end fraction close parentheses times sin open parentheses straight pi over 4 close parentheses plus cos open parentheses fraction numerator 3 straight pi over denominator 4 end fraction close parentheses times cos open parentheses straight pi over 4 close parentheses end cell row blank equals cell sin open parentheses straight pi minus straight pi over 4 close parentheses times sin open parentheses straight pi over 4 close parentheses plus cos open parentheses straight pi minus straight pi over 4 close parentheses times cos open parentheses straight pi over 4 close parentheses end cell row blank equals cell sin open parentheses straight pi over 4 close parentheses times sin open parentheses straight pi over 4 close parentheses minus cos open parentheses straight pi over 4 close parentheses times cos open parentheses straight pi over 4 close parentheses end cell row blank equals cell open parentheses sin open parentheses straight pi over 4 close parentheses close parentheses squared minus open parentheses cos open parentheses straight pi over 4 close parentheses close parentheses squared end cell row blank equals cell open parentheses 1 half square root of 2 close parentheses squared minus open parentheses 1 half square root of 2 close parentheses squared end cell row blank equals 0 end table  

Jadi, nilai sin open parentheses fraction numerator 3 straight pi over denominator 4 end fraction close parentheses times sin open parentheses straight pi over 4 close parentheses plus cos open parentheses fraction numerator 3 straight pi over denominator 4 end fraction close parentheses times cos open parentheses straight pi over 4 close parentheses equals 0

76

4.2 (4 rating)

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