Suppose sin(θ)=2x/5 for some acute angle θ. Express in terms of x

a) ln|secθ+tanθ|
b) sin2θ
c) θ

sin(θ) = 2x/5
Opposite = 2x, and Hypotenues = 5

Adjasent = sqrt[5^2 -(2x)^2] = sqrt(25 -4x^2)

a)
ln|secθ+tanθ| = ln[(1+sinθ)/cosθ]
= ln[(1+2x/5)/sqrt(25-4x^2)/5] =
= ln[(5+2x) / sqrt(25-4x^2)] >===============< ANSWER

b)
sin2θ = 2sinθ.cosθ = 2(2x/5)[sqrt(25-4x^2)/5]

sin2θ = 4x / sqrt(25 -4x^2) >=================< ANSWER

c)
θ = arcsin(2x/5) degrees >================< ANSWER