Given that tan x = \(\frac{2}{3}\), where 0o d” x d” 90o, Find the value of 2sinx.
- \(\frac{2\sqrt{13}}{13}\)
- \(\frac{3\sqrt{13}}{13}\)
-
\(\frac{4\sqrt{13}}{13}\)
- \(\frac{6\sqrt{13}}{13}\)
The correct answer is: C
Explanation
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\(\frac{2}{\sqrt{13}}\)
= \(\frac{4}{\sqrt{13}}\)
= \(\frac{4}{\sqrt{13}} = \frac{\sqrt{13}}{\sqrt{13}}\)
= \(\frac{4\sqrt{13}}{13}\)
There is an explanation video available .