Diketahui , dengan maka nilai

Pertanyaan

Diketahui $tan space straight A equals negative 1 half$ , dengan $straight pi over 2 less than straight A less than straight pi$ maka nilai $sin space straight A times cos space straight A equals....$

Pembahasan Soal:

Diketahui $tan space straight A equals negative 1 half$ ,

Misalkan: $tan space straight A equals y over x$ , sehingga

$table attributes columnalign right center left columnspacing 0px end attributes row r equals cell square root of x squared plus y squared end root end cell row blank equals cell square root of open parentheses negative 1 close parentheses squared plus 2 squared end root end cell row blank equals cell square root of 1 plus 4 end root end cell row blank equals cell square root of 5 end cell end table$

dengan $straight pi over 2 less than straight A less than straight pi$ artinya sudut A berada diantara $90 degree$ dan $180 degree$ atau sudut A berada di kuadran II.

$sin$ di kuadran II bernilai positif

$sin space straight A equals y over r equals fraction numerator 1 over denominator square root of 5 end fraction$

$cos$ di kuadran II bernilai negatif

$cos space straight A equals x over r equals negative fraction numerator 2 over denominator square root of 5 end fraction$

Maka,

$table attributes columnalign right center left columnspacing 0px end attributes row cell sin space straight A times cos space straight A end cell equals cell fraction numerator 1 over denominator square root of 5 end fraction times open parentheses negative fraction numerator 2 over denominator square root of 5 end fraction close parentheses end cell row blank equals cell negative 2 over 5 end cell end table$

Jadi, nilai $sin space straight A times cos space straight A equals negative 2 over 5$ .

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 03 Juni 2021

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