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

A.

\(\frac{2\sqrt{13}}{13}\)

B.

\(\frac{3\sqrt{13}}{13}\)

C.

\(\frac{4\sqrt{13}}{13}\)

D.

\(\frac{6\sqrt{13}}{13}\)

Correct answer is C

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\(\frac{2}{\sqrt{13}}\)

= \(\frac{4}{\sqrt{13}}\)

= \(\frac{4}{\sqrt{13}} = \frac{\sqrt{13}}{\sqrt{13}}\)

= \(\frac{4\sqrt{13}}{13}\)