Question

If x is an acute angle and tan x = 5, find the exact value of the trigonometric function sin x.

• A. $3/\sqrt{26}$
• B. $1/\sqrt{26}$
• C. $5/\sqrt{27}$
• D. $5/\sqrt{26}$

Answer 1

The correct option is D

$5/\sqrt{26}$

If tan x = opposite / adjacent = 5 = 5 / 1, then we can say that opposite = 5 and adjacent = 1 and find the hypotenuse using Pythagora's theorem.

$hypotenus{e}^2=adjacen{t}^2+opposit{e}^2$

$hypotenus{e}^2=1^2+5^2$

hypotenuse = $\sqrt{26}$

We now use trigonometric ratios to find

sin x = opposite / hypotenuse =$5/\sqrt{26}$