WMA11 Jan 2022

9. WMA11/01 Edexcel IAL P1 January 2022, Q9 (Trignometric Ratios: Transforming Trigonometric Graphs)

Figure 4 shows part of the curve with equation​​ 

y = Acos(x – 30)°

where A is a constant.​​ 

The​​ point P is a minimum point on the curve and has coordinates (30, –3) as shown in Figure 4.​​ 

(a) Write down the value of A.​​ 

(1)

The point Q is shown in Figure 4 and is a maximum point.​​ 

(b) Find the coordinates of Q.​​ 

(3)

SOLUTION​​ 

a-​​ 

The value of A represents the amplitude of the graph. In this case, the amplitide or A is -3 as the y-coordinate of P, which is the minimum point on the graph, is -3. Moreover, it is also the reflecion of cosine graph.

Thus, the value of A is

A=-3

b-​​ 

x-coordinate of Q=30 units to right+1st cycle+2nd cycle+half cycle

x-coordinate of Q=30+360+360+180

x-coordinate of Q=210+720

x-coordinate of Q=930

The coordinates of​​ maximum point Q is (930,3).​​