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 AQA A Level Maths 1.8 E: Trigonometry, 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. Each one has a worked solution and a mark scheme showing where the marks go.