The vertical displacement ddd (in mm) of a tuning fork's prong over a cycle is modeled by the function
d=sinθ∘ d = \sin \theta^\circ d=sinθ∘for −360≤θ≤360-360 \le \theta \le 360−360≤θ≤360.
A point A A\,A on the displacement curve has coordinates (a,−32)(a, -\frac{\sqrt{3}}{2})(a,−23).
(i) Determine the value of aaa, given that −180<a<−90-180 < a < -90−180<a<−90.
(ii) State the value of sin(a∘+720∘)\sin(a^\circ + 720^\circ)sin(a∘+720∘).
A second point B B\,B on the curve has coordinates (b,37)(b, \frac{3}{7})(b,73), where 0<b<900 < b < 900<b<90.
(i) Find the exact value of sin(b∘−180∘)\sin(b^\circ - 180^\circ)sin(b∘−180∘).
(ii) Find the exact value of cosb∘\cos b^\circcosb∘.
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.