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Given that tan x = $\frac{2}{3}$ , where 0^o d" x...

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

A.

$\frac{2\sqrt{13}}{13}$

B.

$\frac{3\sqrt{13}}{13}$

C.

$\frac{4\sqrt{13}}{13}$

D.

$\frac{6\sqrt{13}}{13}$

View answer & explanation

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 $\frac{2}{\sqrt{13}}$

= $\frac{4}{\sqrt{13}}$

= $\frac{4}{\sqrt{13}} = \frac{\sqrt{13}}{\sqrt{13}}$

= $\frac{4\sqrt{13}}{13}$

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