The number of real solutions ( x , y ) where | y |= sin x, y= cos -1( cos x),-2 π ≤ x ≤ 2 π, is

Question

The number of real solutions ( x , y ) where | y |= sin x, y= cos -1( cos x),-2 π ≤ x ≤ 2 π, is (A) 2 (B) 1 (C) 3 (D) 4

Tardigrade Admin · Accepted Answer

Graph of |y|= sin x and y= cos -1( cos x) are shown in fig. It is evident from the graph that the curves intersect at (0,0),(2 π, 0) and (-2 π, 0). Hence, there are 3 solutions.

Q. The number of real solutions $(x, y)$ where $∣ y ∣ = sin x$ , $y = cos^{- 1} (cos x), - 2 π \leq x \leq 2 π$ , is

2

1

3

4

Graph of $∣ y ∣ = sin x$ and $y = cos^{- 1} (cos x)$ are shown in fig. It is evident from the graph that the curves intersect at $(0, 0), (2 π, 0)$ and $(- 2 π, 0)$ .
Hence, there are $3$ solutions.

Q. The number of real solutions (x,y) where ∣y∣=sinx, y=cos−1(cosx),−2π≤x≤2π, is

2

1

3

4

Graph of ∣y∣=sinx and y=cos−1(cosx) are shown in fig. It is evident from the graph that the curves intersect at (0,0),(2π,0) and (−2π,0). Hence, there are 3 solutions.

Q. The number of real solutions $(x, y)$ where $∣ y ∣ = sin x$ , $y = cos^{- 1} (cos x), - 2 π \leq x \leq 2 π$ , is

Graph of $∣ y ∣ = sin x$ and $y = cos^{- 1} (cos x)$ are shown in fig. It is evident from the graph that the curves intersect at $(0, 0), (2 π, 0)$ and $(- 2 π, 0)$ .
Hence, there are $3$ solutions.