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 (MEI) A Level Maths 1.7 Trigonometry, covering 1.7.1 Solve right-angled triangles, 1.7.2 Definitions of sin, cos and tan for any angle, 1.7.3 Graphs of sin, cos and tan, 1.7.4 Exact values of trig functions (degrees), 1.7.5 Area of a triangle, 1.7.6 Sine and cosine rules, 1.7.7 Identity tan = sin/cos, 1.7.8 Identity sin^2 + cos^2 = 1, 1.7.9 Solve simple trigonometric equations, 1.7.10 Exact values of trig functions (radians) (A-level only), 1.7.11 Inverse trigonometric functions (A-level only), 1.7.12 Radians and degree conversion (A-level only), 1.7.13 Arc length and area of a sector (A-level only), 1.7.14 Small angle approximations (A-level only), 1.7.15 Sec, cosec and cot functions (A-level only), 1.7.16 Graphs of reciprocal trig functions (A-level only), 1.7.17 Pythagorean identities for sec and cosec (A-level only), 1.7.18 Compound angle formulae (A-level only), 1.7.19 Double angle identities (A-level only), 1.7.20 Expressions for a cos θ ± b sin θ (A-level only), 1.7.21 Use identities to solve equations (A-level only), 1.7.22 Proofs involving trigonometric functions (A-level only), 1.7.23 Trig to solve problems in context (A-level only), and 1.7 Trigonometry. Each one has a worked solution and a mark scheme showing where the marks go.