Skip to content

Course home

1.7 Trigonometry

1.7 Trigonometry

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209
Question 190

The angular displacement of a pendulum, Θ\ThetaΘ, is modelled by the function Θ(t)=cos⁡t\Theta(t) = \cos tΘ(t)=cost, where ttt is the time in seconds measured from the equilibrium position. A specific displacement ppp is recorded at time t=ϕt = \phit=ϕ, where 0<ϕ<π20 < \phi < \frac{\pi}{2}0<ϕ<2π​, such that cos⁡ϕ=p\cos \phi = pcosϕ=p.

a.

State, in terms of ppp, the value of: (i) 10cos⁡(2π−ϕ)10 \cos (2\pi - \phi)10cos(2π−ϕ) (ii) cos⁡(ϕ−π)\cos (\phi - \pi)cos(ϕ−π) (iii) 0.5+cos⁡(−ϕ)0.5 + \cos (-\phi)0.5+cos(−ϕ)

[3]
b.

Sketch the graph of y=cos⁡2ty = \cos 2ty=cos2t for the interval 0≤t≤π0 \le t \le \pi0≤t≤π, labelling the coordinates of the points where the curve meets the axes and any stationary points.

[2]
c.

Determine, in terms of ϕ\phiϕ, the ttt-coordinates of any points in the interval 0<t<π0 < t < \pi0<t<π for which cos⁡2t=p\cos 2t = pcos2t=p.

[2]
Markscheme

1.7 Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.7 Trigonometry

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.

Question bank