Question

The angle of intersection of the curves y² = 2x/π and y = sinx, is

• A. cot^-1(-1/π)
• B. cot^-1π
• C. cot^-1(-π)
• D. cot^-1(1/π)

Answer 1

Answer: (B)

cot^-1π

Answer 2

The curves y² = 2x/π and y = sinx intersect at (0, 0) and (π/2,1). Let the gradients of the tangents to the curves be m₁ and m₂ respectively.

Then m₁ = $\frac{dy}{dx} = \frac{1}{\pi y}$ and m₂ = $\frac{dy}{dx} = \cos x$.

At (π/2,1), m₁ = 1/π,

m₂ = cos$\frac{\pi}{2} =$0

Thus tanθ = $\frac{(1/\pi) - 0}{1 + (1/\pi)(0)} = \frac{1}{\pi} \Rightarrow \theta = \cot^{- 1}\pi$