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.
State the yyy-coordinate of CCC.
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.
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.
The total operational area CBEDCBEDCBED consists of the sector BCEBCEBCE joined to the triangle CDECDECDE.
Calculate the exact area of the region 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.