Express 3cosx+2sinx3\cos x + 2\sin x3cosx+2sinx in the form Rcos(x−α)R\cos(x - \alpha)Rcos(x−α), where R>0R > 0R>0 and 0<α<π20 < \alpha < \frac{\pi}{2}0<α<2π. Give the exact value of RRR and the value of α\alphaα, in radians, to 3 decimal places.
A researcher is monitoring the depth of water in a tidal harbor. The depth of the water, DDD meters, is modeled by the equation
D=154+3cos(0.4t)+2sin(0.4t),0≤t≤12 D = \frac{15}{4 + 3\cos(0.4t) + 2\sin(0.4t)}, \quad 0 \le t \le 12 D=4+3cos(0.4t)+2sin(0.4t)15,0≤t≤12where ttt is the number of hours after midnight.
Find, according to the model: the minimum depth of the water in the harbor, giving your answer to 2 decimal places,
the value of ttt, to 2 decimal places, when D=3.5D = 3.5D=3.5.
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.