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 (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.