A robotic sensor measures the tilt angle β\betaβ (in radians) of a pivoting solar tracker. The relationship between the sensor's input ratio rrr and the tilt angle is given by the function β=arccos(r)\beta = \arccos(r)β=arccos(r) for the domain −1≤r≤1-1 \le r \le 1−1≤r≤1.
Identify the correct graph of β\betaβ against rrr from the following descriptions:
Graph A: A strictly decreasing curve starting at the point (−1,π)(-1, \pi)(−1,π), passing through the point (0,π2)(0, \frac{\pi}{2})(0,2π), and terminating at the point (1,0)(1, 0)(1,0).
Graph B: An S-shaped curve passing through the origin (0,0)(0, 0)(0,0) with endpoints at (−1,−π2)(-1, -\frac{\pi}{2})(−1,−2π) and (1,π2)(1, \frac{\pi}{2})(1,2π).
Graph C: A strictly increasing curve starting at the point (−1,0)(-1, 0)(−1,0), passing through the point (0,π2)(0, \frac{\pi}{2})(0,2π), and terminating at the point (1,π)(1, \pi)(1,π).
Graph D: A curve with horizontal asymptotes at β=π2\beta = \frac{\pi}{2}β=2π and β=−π2\beta = -\frac{\pi}{2}β=−2π, passing through the origin (0,0)(0, 0)(0,0).
