Given that \( \tan x = \frac{2}{3} \), where \(0^\circ < x < 90^\circ\), Find the value of \(2\sin x\).

Assessment: JAMB UTME - Mathematics - 2015 Subject: General Mathematics

Question 1 Report

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

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

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

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

Answer Details

tan x =

\frac{2}{3}

(given), is illustrated in a right-angled

Δ

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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