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1.7 Trigonometry

1.7 Trigonometry

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Question 200

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

1.7 Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.7 Trigonometry

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.

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