Given that sin x 2/3 and is an acute angle find tan x

Answer 1

We can start by using the Pythagorean identity:

sin^2 x + cos^2 x = 1

Since sin x is given as 2/3, we can solve for cos x:

(2/3)^2 + cos^2 x = 1

4/9 + cos^2 x = 1

cos^2 x = 5/9

Taking the positive square root since x is an acute angle:

cos x = √(5/9)

Now we can use the tangent identity:

tan x = sin x/cos x

Substituting the values we know:

tan x = (2/3)/√(5/9)

Rationalizing the denominator:

tan x = (2/3)√(9/5)

tan x = (2/3)(3/√5)

tan x = 2√5/5