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1.5 Trigonometry

1.5 Trigonometry

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Question 204

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.

a.

State the yyy-coordinate of CCC.

[1]
b.

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.

[3]
c.

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.

[2]
d.

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.

[4]
Markscheme

1.5 Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.5 Trigonometry

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.

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