NSW Mathematics Advanced (2 Unit)
Trigonometric Transformations
Period • Amplitude • Phase • Vertical Shift • Modelling
Questions from HSC and trials (2018–2023). Solutions follow.
QUESTIONS
1. What is the amplitude of y = −3 sin(2x)? (1)
2. Find the period of y = cos(3x). (1)
3. y = tan(bx) has period π4 . Find b. (1)
4. What is the phase shift of y = sin(x − π3 )? (1)
5. Describe the transformation from y = cos x to y = cos x − 2. (1)
6. Describe the transformations mapping y = sin x to y = sin(2x + π). (2)
. (2)
7. State the amplitude and period of y = 4 sin πx
2
8. A sinusoidal function has max 5 and min -1. Find amplitude. (1)
9. Find the midline of y = 2 cos x + 3. (1)
10. Reflect y = sin x in x-axis then compress horizontally by factor 12 . (2)
11. Find the phase shift of y = cos(2x + π2 ). (2)
12. Ferris wheel model (radius 10, centre 12, period 40). Write h(t). (3)
13. Write a sine equation: amplitude 3, period 2π, shift π6 right. (2)
1
WORKED SOLUTIONS
Q1 Amplitude
Amplitude = |a| = 3
4
2
1
2
3
4
5
6
4
5
6
−2
−4
Q2 Period
2π
3
T =
1
1
2
3
−1
Q3
π
π
= ⇒b=4
b
4
Q4 Phase Shift
Shift =
π
right
3
2
1
1
2
3
4
−1
Q5
Shift down 2 units.
Q6
y = sin(2(x +
π
))
2
Compression + shift left π2
Q7
Amplitude = 4,
T =4
Q8
5 − (−1)
=3
2
Q9
Midline: y = 3
Q10
y = − sin(2x)
Q11
y = cos(2(x +
π
))
4
Shift left π4
Q12
h = 10 sin
Q13
3
πt
20
+ 12
5
6
π
y = 3 sin x −
6
4