Phase Shift
Horizontal translation of a wave.
Key idea
Horizontal translation of a wave.
In depth
In y = sin(Bx − C), the graph shifts horizontally by C/B. Factor out B first: sin(B(x − C/B)). A positive result is a shift to the right.
Worked example
y = sin(2x − π) = sin(2(x − π/2)), shifted π/2 right.
Formula
Real-world uses
- Aligning two signals in electronics and audio
- Timing signals in communications
Common mistake
Shifting by C without dividing by B.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Phase Shift?
Horizontal translation of a wave. It is a topic at the advanced level in Trigonometry.
What is the formula for Phase Shift?
The key formula is y = sin(x − φ).
Where is Phase Shift used in real life?
Real-world examples: Aligning two signals in electronics and audio; Timing signals in communications.
What should I learn before Phase Shift?
Make sure you are comfortable with Period and Frequency, the previous topic in Trigonometry.
What is a common mistake with Phase Shift?
Shifting by C without dividing by B.
How can I practise Phase Shift?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Phase Shift?
Move on to Vertical Shift and Midline next.
Related advanced topics in Trigonometry
- Graph of Tangent – Periodic with vertical asymptotes at odd multiples of π/2.
- Vertical Shift and Midline – Moves the wave up or down.
- General Sinusoid – Combine amplitude, period, phase and shift.
- Graphs of Reciprocal Trig Functions – Secant, cosecant and cotangent graphs.
- Pythagorean Identity – The key identity from the unit circle.
- Other Pythagorean Identities – Divide the identity by sin² or cos².