Skip to content

Course home

Sign up

1.8 E: Trigonometry

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169
Question 156

It is given that

f(x)=3cos⁡x−4sin⁡xf(x) = 3\cos x - 4\sin xf(x)=3cosx−4sinx

and that f(x)=Rcos⁡(x+α)f(x) = R\cos(x + \alpha)f(x)=Rcos(x+α), where R>0 R > 0\,R>0 and 0°≤α≤90°0° \leq \alpha \leq 90°0°≤α≤90°.

a.

Find the value of R R\,R and the value of α\alphaα, giving α \alpha\,α to one decimal place.

[3]
b.

Hence solve, for 0°≤x≤360°0° \leq x \leq 360°0°≤x≤360°, the equation

3cos⁡x−4sin⁡x=13\cos x - 4\sin x = 13cosx−4sinx=1

Give your answers to one decimal place.

[4]
Markscheme

1.8 E: Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.8 E: Trigonometry

317 exam-style questions on AQA A Level Maths 1.8 E: Trigonometry, covering 1.8.1 Trigonometric definitions, rules and radians, 1.8.2 Small angle approximations (A-level only), 1.8.3 Trigonometric functions and exact values, 1.8.4 Reciprocal and inverse trigonometric functions (A-level only), 1.8.5 Trigonometric identities, 1.8.6 Compound and double angle formulae (A-level only), 1.8.7 Solving trigonometric equations, 1.8.8 Proofs with trigonometric identities, and 1.8.9 Trigonometry in context. Each one has a worked solution and a mark scheme showing where the marks go.

Question bank