Trig Graph Transformations
Stretch, compress, reflect and shift trigonometric graphs.
Key idea
Stretch, compress, reflect and shift trigonometric graphs.
In depth
Combine stretches, shifts and reflections: y = a·f(b(x − c)) + d. Work from the inside: horizontal changes alter the period and shift, vertical changes alter the amplitude and midline.
Worked example
y = −2 cos(3x) + 1: amplitude 2, flipped, period 2π/3, midline 1.
Formula
Real-world uses
- Adjusting sound waves and seasonal models by stretching and shifting the curves
Common mistake
Applying a horizontal shift before factoring b out.
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 Trig Graph Transformations?
Stretch, compress, reflect and shift trigonometric graphs. It is a topic at the advanced level in Trigonometry.
What is the formula for Trig Graph Transformations?
The key formula is y = a sin(bx)+c.
Where is Trig Graph Transformations used in real life?
Real-world examples: Adjusting sound waves and seasonal models by stretching and shifting the curves.
What should I learn before Trig Graph Transformations?
Make sure you are comfortable with Parametric Unit Circle, the previous topic in Trigonometry.
What is a common mistake with Trig Graph Transformations?
Applying a horizontal shift before factoring b out.
How can I practise Trig Graph Transformations?
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 Trig Graph Transformations?
Move on to Solving Triangles in Surveying 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.
- 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.