Pertanyaan

sin 4 5 π + cos 4 5 π = ....

$sin \frac{5 π}{4} + cos \frac{5 π}{4} =$ ....

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S. Nur

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Jawaban terverifikasi

Pembahasan

Perhatikan bahwa Karena sudut berada di kuadran III, maka dan bernilai negatif. Oleh karena itu, kita dapatkan dan Oleh karena itu, kita dapatkan bahwa Jadi, jawaban yang tepat adalah E.

Perhatikan bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin invisible function application fraction numerator 5 straight pi over denominator 4 end fraction end cell equals cell sin invisible function application open parentheses straight pi plus straight pi over 4 close parentheses end cell row cell cos invisible function application fraction numerator 5 straight pi over denominator 4 end fraction end cell equals cell cos invisible function application open parentheses straight pi plus straight pi over 4 close parentheses end cell row blank blank blank end table end style$

Karena sudut $begin mathsize 14px style fraction numerator 5 straight pi over denominator 4 end fraction end style$ berada di kuadran III, maka $begin mathsize 14px style sin invisible function application fraction numerator 5 straight pi over denominator 4 end fraction end style$ dan $begin mathsize 14px style cos invisible function application fraction numerator 5 straight pi over denominator 4 end fraction end style$ bernilai negatif. Oleh karena itu, kita dapatkan

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin invisible function application fraction numerator 5 straight pi over denominator 4 end fraction end cell equals cell sin invisible function application open parentheses straight pi plus straight pi over 4 close parentheses end cell row blank equals cell negative sin invisible function application straight pi over 4 end cell row blank equals cell negative 1 half square root of 2 end cell end table end style$

dan

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos invisible function application fraction numerator 5 straight pi over denominator 4 end fraction end cell equals cell cos invisible function application open parentheses straight pi plus straight pi over 4 close parentheses end cell row blank equals cell negative cos invisible function application straight pi over 4 end cell row blank equals cell negative 1 half square root of 2 end cell end table end style$

Oleh karena itu, kita dapatkan bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin invisible function application fraction numerator 5 straight pi over denominator 4 end fraction plus cos invisible function application fraction numerator 5 straight pi over denominator 4 end fraction end cell equals cell negative 1 half square root of 2 minus 1 half square root of 2 end cell row blank equals cell negative square root of 2 end cell end table end style$

Jadi, jawaban yang tepat adalah E.