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Edexcel A-Level Mathematics AS P1.3 Trigonometry Questions

Practise triangle trigonometry, radian sector formulae and trig graphs, linking diagrams, functions and real contexts to exact calculations.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
AS

Exam points

  • choose sine rule, cosine rule or 1/2ab sin C from the triangle information given
  • use s=rθ and A=1/2r^2θ to find arc lengths, sectors, perimeters and areas
  • read periods, coordinates and transformations from sine, cosine and tangent graphs

Covered syllabus points

P1.3.1 - Sine rule, cosine rule and triangle areaP1.3.2 - Radian measure,P1.3.3 - Trigonometric functions and graphs

Question 1

[Maximum number: 10]
Figure 1

Figure 1

Figure 1 shows the plan view for the design of a stage.
The design consists of a sector OBC of a circle, with centre O, joined to two congruent triangles OAB and ODC.

Given that
- angle B O C=2.4 radians
- area of sector BOC=40 m2B O C=40 \mathrm{~m}^{2}
- AOD is a straight line of length 12.5 m

Question (a)

(a)

find the radius of the sector, giving your answer, in m , to 2 decimal places,

[ 2 ]

Question (b)

(b)

find the size of angle AOB, in radians, to 2 decimal places.

Hence find

[ 1 ]

Question (c)

(c)

the total area of the stage, giving your answer, in m2\mathrm{m}^{2}, to one decimal place,

[ 3 ]

Question (d)

(d)

the total perimeter of the stage, giving your answer, in m , to one decimal place.

[ 4 ]

Question 2

[Maximum number: 2]
Figure 2

Figure 2

Figure 2 shows a plot of part of the curve C1C_{1} with equation

y=5cos⁡xy=5 \cos x

with x being measured in degrees.
The point P, shown in Figure 2, is a minimum point on C1C_{1}

State the coordinates of P

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