Question

Find the angle of intersection of curves,

y = [| sin x | + | cos x |] and x² + y² = 5 where [·] denotes greatest integral function–

• A. tan^–1(2)
• B. tan^–1(1)
• C. tan^–1(4)
• D. None of these

Answer 1

Answer: (A)

tan^–1(2)

Answer 2

We know that,

1 £ | sin x | + | cos x | £ $\sqrt{2}$

\ y = [| sin x | + | cos x |] = 1

Let P and Q be the points of intersection of given curves.

Clearly the given curves meet at points where y = 1

so, we get

x² + 1 = 5

x = ±2

Now, P (2, 1) and Q (–2, 1))

Now, x² + y² = 5

Differentiating the above equation w.r. t. x, we get

2x + 2y $\frac{dy}{dx}$ = 0

̃ $\frac{dy}{dx}$ = –$\frac{x}{y}$

$\left( \frac{dy}{dx} \right)_{(2,1)}$= – 2 and $\left( \frac{dy}{dx} \right)_{(–2,1)}$ = 2

Clearly the slope of line y = 1 is zero and the slope of the tangents at P and Q are (–2) and (2) respectively.

Thus, the angle of intersection is tan^–1(2).