In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
In a study of harmonic oscillations, the phase angle ϕ\phiϕ (in degrees) of a combined wave satisfies the equation
3sin(ϕ+45∘)=2cos(ϕ−60∘) 3 \sin(\phi + 45^\circ) = 2 \cos(\phi - 60^\circ) 3sin(ϕ+45∘)=2cos(ϕ−60∘)Show that
tanϕ=2−33−6 \tan \phi = \frac{\sqrt{2} - 3}{3 - \sqrt{6}} tanϕ=3−62−3Hence or otherwise, solve, for 0∘≤θ<180∘0^\circ \le \theta < 180^\circ0∘≤θ<180∘,
3sin(3θ+45∘)=2cos(3θ−60∘) 3 \sin(3\theta + 45^\circ) = 2 \cos(3\theta - 60^\circ) 3sin(3θ+45∘)=2cos(3θ−60∘)giving your answers to one decimal place.
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.