We have
[tex] \sin 2 \theta = 2 \sin \theta \cos \theta [/tex]
We already know [tex] \sin \theta [/tex] so we have to find [tex] \cos \theta [/tex].
Theta is in the first quadrant so we choose the positive sign:
[tex]\cos \theta = \sqrt{1 - (2/5)^2} = \sqrt{21/25} = \frac 1 5\sqrt{21}[/tex]
[tex] \sin 2 \theta = 2 (\frac 2 5)(\frac 1 5 \sqrt{21}) = \dfrac{4 \sqrt{21}}{25} [/tex]
Choice c
