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 (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.