Solve, for 0<θ<360∘0 < \theta < 360^\circ0<θ<360∘, the equation
4sin(θ+40∘)=3cos(θ+40∘) 4 \sin(\theta + 40^\circ) = 3 \cos(\theta + 40^\circ) 4sin(θ+40∘)=3cos(θ+40∘)giving your answers to one decimal place.
Show that the equation
2sin3x=6sinx−5sinxcosx 2 \sin^3 x = 6 \sin x - 5 \sin x \cos x 2sin3x=6sinx−5sinxcosxcan be written in the form
sinx(acos2x+bcosx+c)=0 \sin x (a \cos^2 x + b \cos x + c) = 0 sinx(acos2x+bcosx+c)=0where aaa, bbb and ccc are constants to be found.
Hence solve for −π≤x≤π-\pi \le x \le \pi−π≤x≤π the equation
2sin3x=6sinx−5sinxcosx 2 \sin^3 x = 6 \sin x - 5 \sin x \cos x 2sin3x=6sinx−5sinxcosxgiving your answers to two decimal places where appropriate.
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.