Cos θ = x/x+1.

Question

 Find an expression in x for sin θ.?

Answer 1

cos(θ) = x/(x + 1)

From the basic trigonometric ratios, cos(θ) = (adjacent side/hypotenuse)

From Pythagorean theorem,

Opposite side = √[(hypotenuse)² - (adjacent side)²]

= √[(x + 1)² - (x)²]

= √[(x² + 1 + 2x - x²]

= √(2x + 1)

sin(θ) = opposite side/hypotenuse

sin(θ) = √(2x + 1)/(x + 1).