Verified answer

Divide by 4 to get x/4 = sin(θ)

Since sin = opposite / hypotenuse, sketch a right triangle and label the hypotenuse 4 and one leg x.

Cos = adjacent / hypotenuse, so solve for the missing side of the triangle using the pythagorean formula.

x^2 + (adjacent)^2 = 4^2

So the adjacent side becomes the square root of (16 – x^2)

Therefore, cos(θ) = [square root of (16 – x^2)] / 4

Hope that helps!

Given that x = 4sin(θ) then we know that sin θ = x/4 so

cos θ = ±√[1 -(x/4)²] using the Pythag theorem: sin² a + cos² a =1

sin(θ) = x/4

θ = arcsin(x/4)

cos(θ) = cos[arcsin(x/4)]

= √(1 - x^2/16)

= √(16 - x^2) / 4