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1.5 Trigonometry

1.5 Trigonometry

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Question 188
57%

The track of a high-precision robot follows a straight line l1l_1l1​ with equation x+4y=32x + 4y = 32x+4y=32. The line l1l_1l1​ intersects the yyy-axis at the point CCC.

a.

State the yyy-coordinate of CCC.

[1]
b.

The point D(8,6)D(8, 6)D(8,6) lies on l1l_1l1​. The line l2l_2l2​ passes through DDD and is perpendicular to l1l_1l1​. The line l2l_2l2​ intersects the yyy-axis at the point EEE.

Show that the yyy-coordinate of EEE is −26-26−26.

[3]
c.

A circular cleaning region BCEBCEBCE, which is a sector of a circle with centre CCC, is used by the robot. Given that angle BCEBCEBCE is 0.80.80.8 radians,

find the length of the arc BEBEBE.

[2]
d.

The total operational area CBEDCBEDCBED consists of the sector BCEBCEBCE joined to the triangle CDECDECDE.

Calculate the exact area of the region CBEDCBEDCBED.

[3]
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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