Vertical Shift and Midline
Moves the wave up or down.
Key idea
Moves the wave up or down.
In depth
Adding D, y = sin x + D shifts the wave up by D, putting the midline at y = D. The maximum is D + A and the minimum is D − A. Tides and temperatures fit this model.
Worked example
y = 2 sin x + 5 oscillates between 3 and 7 around the midline y = 5.
Formula
Real-world uses
- Modelling daily temperature with an average value plus a seasonal swing
Common mistake
Mixing up the midline with the maximum value.
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 Vertical Shift and Midline?
Moves the wave up or down. It is a topic at the advanced level in Trigonometry.
What is the formula for Vertical Shift and Midline?
The key formula is y = sin x + D.
Where is Vertical Shift and Midline used in real life?
Real-world examples: Modelling daily temperature with an average value plus a seasonal swing.
What should I learn before Vertical Shift and Midline?
Make sure you are comfortable with Phase Shift, the previous topic in Trigonometry.
What is a common mistake with Vertical Shift and Midline?
Mixing up the midline with the maximum value.
How can I practise Vertical Shift and Midline?
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 Vertical Shift and Midline?
Move on to General Sinusoid next.
Related advanced topics in Trigonometry
- Graph of Tangent – Periodic with vertical asymptotes at odd multiples of π/2.
- Phase Shift – Horizontal translation of a wave.
- 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.