If the square root of 16-x^2 is expressed as a trigonometric function of x without radicals, letting x=4sin(Θ), evaluate tan(Θ) in terms of x.

Question

Assume that 0<Θ<π/2.

Answer 1

If x = 4sinθ, then sinθ = x/4.

draw a right triangle with acute angle θ, label the side opposite θ as x, and label the hypotenuse as 4. By the Pythagorean Theorem, the side adjacent to θ is √(16 - x²).

So, tanθ = x / √(16 - x²).