Given that tan x = (frac{2}{3}), where 0o d” x d” 90o, Find the value of 2sinx.
-
A.
(frac{2sqrt{13}}{13}) -
B.
(frac{3sqrt{13}}{13}) -
C.
(frac{4sqrt{13}}{13}) -
D.
(frac{6sqrt{13}}{13})
Correct Answer: Option 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{4sqrt{13}}{13})
There is an explanation video available below.