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.
Practise AQA A Level Maths 1.8 E: Trigonometry with exam-style questions for A Level Maths. 239 questions covering 1.8.1 Trigonometric definitions, rules and radians, 1.8.2 Small angle approximations (A-level only), 1.8.3 Trigonometric functions and exact values, 1.8.4 Reciprocal and inverse trigonometric functions (A-level only), 1.8.5 Trigonometric identities, 1.8.6 Compound and double angle formulae (A-level only), 1.8.7 Solving trigonometric equations, 1.8.8 Proofs with trigonometric identities, and 1.8.9 Trigonometry in context, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
