Skip to content

Course home

3.5 Trigonometry (A-level only)

3.5 Trigonometry (A-level only)

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152
Question 60

Let f(x)=6sin⁡xcos⁡x+6cos⁡2x−1f(x) = 6 \sin x \cos x + 6 \cos^2 x - 1f(x)=6sinxcosx+6cos2x−1.

a.

Write f(x)f(x)f(x) in the form

asin⁡2x+bcos⁡2x+c a \sin 2x + b \cos 2x + c asin2x+bcos2x+c

where a,b,a, b,a,b, and ccc are integers to be found.

[3]
b.

Use the answer to part (a) to write f(x)f(x)f(x) in the form

Rsin⁡(2x+α)+c R \sin (2x + \alpha) + c Rsin(2x+α)+c

where R>0R > 0R>0 and 0<α<π20 < \alpha < \frac{\pi}{2}0<α<2π​. Give the exact value of RRR and give the value of α\alphaα in radians to 3 significant figures.

[3]
c.

Hence, or otherwise, (i) state the maximum value of f(x)f(x)f(x), (ii) find the second smallest positive value of xxx at which a maximum value of f(x)f(x)f(x) occurs. Give your answer to 3 significant figures.

[3]
Markscheme

3.5 Trigonometry (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.5 Trigonometry (A-level only)

225 exam-style questions on WJEC A Level Maths 3.5 Trigonometry (A-level only), covering 3.5.1 Trigonometry (A-level only), 3.5.2 Trigonometry (A-level only), 3.5.3 Trigonometry (A-level only), 3.5.4 Trigonometry (A-level only), 3.5.5 Trigonometry (A-level only), 3.5.6 Trigonometry (A-level only), 3.5.7 Trigonometry (A-level only), and 3.5.8 Trigonometry (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

Question bank