Question 28
A plan for an observation deck is shown below. The design consists of a major sector ABCOA ABCOA\,ABCOA of a circle with centre OOO, joined to a triangular viewing platform AODAODAOD. It is given that:
- The radius of the circle OA=OC=10 mOA = OC = 10\text{ m}OA=OC=10 m
- The platform edge AD=22 mAD = 22\text{ m}AD=22 m
- The angle ∠ODA=0.40 radians\angle ODA = 0.40\text{ radians}∠ODA=0.40 radians
- ∠AOD \angle AOD\,∠AOD is an obtuse angle
- OCD OCD\,OCD is a straight line
Find:
a.[3]
the size of angle AODAODAOD, in radians, to 3 decimal places,
b.[2]
the length of arc ABCABCABC, in metres, to one decimal place,
c.[3]
the total area of the deck, in m2\text{m}^2m2, to one decimal place.
1.5 Trigonometry Questions
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.