Given that tan x = 23 2 3 , where 0o d" x d" 90o, Find the value of 2sinx.

Given that tan x = $\frac{2}{3}$, where 0o d" x d" 90o, Find the value of 2sinx.

Answer Details

tan x = $\frac{2}{3}$(given), is illustrated in a right-angled $\Delta$
thus m2 = 22 + 32
= 4 + 9 = 13
m = $\sqrt{13}$
Hence, 2sin x = 2 x $\frac{2}{m}$
2 x$\frac{2}{\sqrt{13}}$
= $\frac{4}{\sqrt{13}}$
= $\frac{4}{\sqrt{13}}=\frac{\sqrt{13}}{\sqrt{13}}$
= $\frac{4\sqrt{13}}{13}$