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Edexcel A-Level Mathematics AS P2.6 Trigonometry Questions

Practise rewriting trigonometric expressions with identities, then solving equations over stated degree or radian intervals with exact or rounded answers.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
AS

Exam points

  • find all solutions in a stated interval, giving degrees or radians to the required accuracy

Covered syllabus points

P2.6.1 - Core trigonometric identitiesP2.6.2 - Solving trigonometric equations

Question 1

[Maximum number: 9]



In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.

Question (a)

(a)

Solve, for 0≤θ<180∘0 \leq \theta < 180^\circ, the equation
7sin⁡2θ=5cos⁡2θ7\sin 2\theta = 5\cos 2\theta
giving your answers, in degrees, to one decimal place.

[ 4 ]

Question (b)

(b)

Solve, for 0≤x<2π0 \leq x < 2\pi, the equation
24tan⁡x=5cos⁡x24\tan x = 5\cos x
giving your answers, in radians, to 3 decimal places.

[ 5 ]

Question 2

[Maximum number: 5]

In this question you must show detailed reasoning.

Solutions relying entirely on calculator technology are not acceptable.

Hence solve for −π2⩽x⩽π2-\frac{\pi}{2} \leqslant x \leqslant \frac{\pi}{2}

(3cos⁡2x−tan⁡2x)cos⁡2x=2(3 \cos 2 x-\tan 2 x) \cos 2 x=2

Question 3

[Maximum number: 4]
Figure 5

Figure 5

Figure 5 shows a sketch of part of the curve C with equation y=sin⁡(x12)y=\sin \left(\frac{x}{12}\right), where x is measured in radians. The point M shown in Figure 5 is a minimum point on C.

Question (a)

(a)

the negative solution of the equation sin⁡(x12)=k\sin \left(\frac{x}{12}\right)=k that is closest to zero,

[ 2 ]

Question (b)

(b)

the smallest positive solution of the equation (x/12)=k.

[ 2 ]
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