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).
317 exam-style questions on OCR A Level Maths 1.5 Trigonometry, covering 1.5.1 Definitions for all arguments, 1.5.2 Sine and cosine rules, 1.5.3 Area of a triangle, 1.5.4 Radian measure (A-level only), 1.5.5 Small angle approximations (A-level only), 1.5.6 Graphs of basic trigonometric functions, 1.5.7 Exact values in radians (A-level only), 1.5.8 Reciprocal and inverse trigonometric ratios (A-level only), 1.5.9 Graphs of reciprocal and inverse functions (A-level only), 1.5.10 Trigonometric identities, 1.5.11 Further trigonometric identities (A-level only), 1.5.12 Double angle and compound angle formulae (A-level only), 1.5.13 Geometrical proofs of formulae (A-level only), 1.5.14 Harmonic form Rcos / Rsin (A-level only), 1.5.15 Trigonometric equations, 1.5.16 Proof involving trigonometric functions (A-level only), and 1.5.17 Trigonometric functions in context. Each one has a worked solution and a mark scheme showing where the marks go.