WMA11 October 2021

7. WMA11/01​​ Edexcel​​ IAL P1 Oct 2021, Q7​​ (Radians &​​ Trigonometry)

Figure 3 shows the design for a sign at a bird sanctuary.​​ 

The design consists of a kite OABC joined to a​​ sector OCXA of a circle centre O.​​ 

In the design​​ 

• OA = OC = 0.6m​​ 

• AB = CB = 1.4m​​ 

• Angle OAB = Angle OCB = 2 radians​​ 

• Angle AOC = θ radians, as shown in Figure 3​​ 

Making your method clear,​​ 

(a) show that θ = 1.64 radians to 3 significant figures,​​ 

(4)

(b) find the perimeter of the sign, in metres to 2 significant figures,​​ 

(2)

(c) find the area of the sign, in m2 to 2 significant figures.​​ 

(4)

SOLUTION​​ 

a-​​ 

Let OB=x. now, using cosine rule to find the side x of traingle as marked above.

a2=b2+c2-2bccos⁡A

x2=0.62+1.42-20.61.4cos⁡2

x=1.7375…

Now, using sine​​ rule to find the angleθ.

sin⁡θ21.4=sin⁡21.7375

sin⁡θ2=1.4sin⁡21.7375…

θ2=0.82219..

θ=2 x 0.82219

θ=1.644…

θ =1.64 median 3sg

b-​​ 

Perimeter is the sum of all external sides of the object.​​ 

P=Arc Length+CB+AB

Where arc length is equal to l=rθ. And, CB=AB=1.4.

P=rθ+CB+AB

P=0.62π-1.64+2(1.4)

P=5.5832…m

P=5.6m  

c- ​​ 

The total area of sign is equal to​​ 

Area=ASector+2ATriangle

Area=12r2θ+212absin⁡θ

Area=12r22π-1.64+2 x120.61.4sin⁡2

Area=120.622π-1.64+0.6 x 1.4sin⁡2

Area=1.59879…

Area=1.6m2