WMA11 Jan 2021

3. WMA11/01​​ Edexcel​​ IAL P1 January 2021 IAL Q3​​ (Trignometric Ratios: Transforming Trignometric Graphs)

Figure 1 shows a sketch of part of the curve C1​​ with equation y = 4cos x°​​ 

The point P and the​​ point Q lie on C1​​ and are shown in Figure 1.​​ 

• State​​ 

• the coordinates of P,​​ 

• the coordinates of Q.​​ 

 (3)

The curve C2​​ has equation y = 4cos x° + k, where k is a constant.​​ 

Curve C2​​ has a minimum y value of –1​​ 

The point R is the maximum point on C2​​ with the​​ smallest positive x coordinate.​​ 

• State the coordinates of R.​​ 

(2)

SOLUTION​​ 

a-​​ 

a- i-​​ 

P-180o,-4

a-​​ ii-​​ 

Q450o,0

b- We know that the range of​​ 

-4≤4cos⁡x≤4

-4+k≤4cos⁡x+k≤4+k

We are told that minimum value of y of Curve C2 is -1, so​​ 

-4+k=-1

k=3

This means that the vertical translation of the graph is 3​​ units. So the y-coordinate would be 4+3=7.​​ 

Hence the​​ the maximum point on C2​​ with the smallest positive x coordinate, hence R must b ethe first peak as marked on the graph below, as it is the point which has the minimum positive value of x-coordinate. Other than that, all remianing points on peak would have greater value of x. ​​ 

Hence, point R is

R 360o,7