Skip to content

Course home

1.7 Trigonometry

1.7 Trigonometry

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209
Question 99

The intensity I I\,I of a laser beam passing through a specific optical filter is modeled by the equation I=5cos⁡2α+sin⁡2αI = 5\cos^2 \alpha + \sin 2\alphaI=5cos2α+sin2α, where α \alpha\,α is the angle of incidence.

a.

Given that I=2I = 2I=2, show that

2tan⁡2α−2tan⁡α−3=0 2\tan^2 \alpha - 2\tan \alpha - 3 = 0 2tan2α−2tanα−3=0
[3]
b.

Hence, find all possible values of α \alpha\,α in the range 0<α<2π 0 < \alpha < 2\pi\,0<α<2π for which the intensity is 2 units. Give your answers to two decimal places.

[4]
c.

Determine the values of x x\,x in the interval 0<x<π3\displaystyle 0 < x < \frac{\pi}{3}0<x<3π​ such that

5cos⁡2(3x+π4)+sin⁡(6x+π2)=2 5\cos^2 \left( 3x + \frac{\pi}{4} \right) + \sin \left( 6x + \frac{\pi}{2} \right) = 2 5cos2(3x+4π​)+sin(6x+2π​)=2

Give your answers to one decimal place.

[3]
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