WMA11 June 2022

• WMA11/01 Edexcel IAL P1 June 2022, Q9​​ (Trigonometric Graphs:​​ ​​ Transformations)

Figure 4 shows part of the graph of the curve with equation y = sin x​​ 

Given that sinα = p, where 0 <​​ α < 90°​​ 

• state, in terms of p, the value of​​ 

• 2sin(180° − α)​​ 

• sin(α − 180°)​​ 

• 3 + sin(180° + α)​​ 

​​ (3)​​ 

A copy of Figure 4, labelled Diagram 1, is shown on page 27. On Diagram 1,​​ 

• sketch the graph of y = sin 2x​​ 

(2)​​ 

• Hence find, in terms of α, the x coordinates of any points in the interval 0 < x < 180° where​​ 

sin 2x = p

(3)

SOLUTION​​ 

a- (i)-​​ The value of sin(180 -​​ α) is p as can be seen from the sketch below.​​ 

So,​​ 

2sin⁡(180- α)=2p

(ii)-​​ The value of sin(α​​ - 180) is - p as can be seen from the sketch below.​​ 

So,​​ 

sin⁡(α-180)=- p

iii-​​ The value of ​​ sin(180+​​ α) is 3 - p as can be seen from the sketch below

So,​​ 

3+sin⁡(180+α)=3- p

b-​​ 

c-​​ After transformation, the value or angle whose sine is equal to p is the half of .​​ 

thus, the two possible solutions are​​ 

x=α2         x=180-α2