Quiz - Universityku

$~$
Materi : Trigonometri
$~$

Jika :
$~$
$tan( alpha ) = frac{2}{3}$
~

Tentukan nilai :

$sin frac{1}{2} alpha$

Quiz

Jawab:

tan A = 2/3 = d/s

d= 2, s =3 , maka m² = d²+ s²

m² = 4 + 9 = 13

m = √13

cos x = s/m = 3/√13

cos x = $sf frac{3}{13}sqrt {13}$

cos x = 1 – 2 sin² 1/2 x

2 sin² 1/2 x = 1 – cos x

sin² 1/2 x = 1/2 -1/2 cos x

sin² 1/2 x = 1/4 (2 – 2 cos x)

sin² 1/2 x = 1/4 [ 2 -6/13 √13]

$sf sinfrac{1}{2}x = pm frac{1}{2}sqrt{2 - frac{6}{13}sqrt {13}}$