Pertanyaan

Diketahui x di kuadran I dan tan x = p 2 . Tentukan nilai sin ( 18 0 ∘ + x ) !

Diketahui $x$ di kuadran I dan $tan x = \frac{2}{p}$ . Tentukan nilai $sin (18 0^{\circ} + x)$ !

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Jawaban terverifikasi

Jawaban

nilai .

nilai $begin mathsize 14px style sin space left parenthesis 180 degree plus x right parenthesis equals fraction numerator 2 square root of p squared plus 4 end root over denominator p squared plus 4 end fraction end style$ .

Pembahasan

Diketahui di kuadran I dan . Untuk sudut lancip, maka merupakan sudut kuadran III.Dalam trigonometri, relasi sudut dinyatakan sebagai berikut: Jadi, nilai .

Diketahui di kuadran I dan .

begin mathsize 14px style 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 p squared plus 2 squared end root end cell row blank equals cell square root of p squared plus 4 end root end cell end table end style

Untuk sudut lancip, maka merupakan sudut kuadran III. Dalam trigonometri, relasi sudut dinyatakan sebagai berikut:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin space left parenthesis 180 degree plus x right parenthesis end cell equals cell negative sin space x end cell row blank equals cell negative y over r end cell row blank equals cell negative fraction numerator 2 over denominator square root of p squared plus 4 end root end fraction times fraction numerator square root of p squared plus 4 end root over denominator square root of p squared plus 4 end root end fraction end cell row blank equals cell negative fraction numerator 2 square root of p squared plus 4 end root over denominator p squared plus 4 end fraction end cell end table end style$

Jadi, nilai $begin mathsize 14px style sin space left parenthesis 180 degree plus x right parenthesis equals fraction numerator 2 square root of p squared plus 4 end root over denominator p squared plus 4 end fraction end style$ .