A coastal surveillance system uses two intersecting paths for its detection beams, p1p_1p1 and p2p_2p2. The primary path p1p_1p1 follows the line with equation 4y+3x=244y + 3x = 244y+3x=24. The path p1p_1p1 intersects the yyy-axis at the point CCC.
State the yyy-coordinate of CCC.
A tracking station is located at the point D(6,1.5)D(6, 1.5)D(6,1.5), which lies on p1p_1p1. A secondary beam p2p_2p2 originates from DDD and is directed perpendicular to p1p_1p1. The beam p2p_2p2 intersects the yyy-axis at the point EEE.
Show that the yyy-coordinate of EEE is −6.5-6.5−6.5.
A circular scanning sector BCEBCEBCE is defined with centre CCC and radius CECECE. Given that the central angle BCEBCEBCE is 0.80.80.8 radians,
find the length of the arc BEBEBE.
The combined detection zone CBEDCBEDCBED is formed by the sector BCEBCEBCE and the triangular region CDECDECDE.
Calculate the exact area of the combined detection zone CBEDCBEDCBED.
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.