# Sinusoidal Transformations: Sine and Cosine

- Author:
- James Kass

Drag the sliders to view transformations of sine and cosine functions.

- Briefly describe how the original sine graph changes when a = 2
- Click the Reset button and describe how the sine graph changes when b = 2
- What value of b will stretch the sine graph to be twice as wide as the original?
- Click the Reset button, uncheck the Sine box and check the Cosine box. What value of b will shorten
- What value of b will shorten the cosine graph to ¼ its original length?
- Click the Reset button and check the Cosine box so that both functions are visible. What happens to the graphs when you make c = π/2 (1.57)?
- Click the Reset. Describe what happens to the graph when d = -2?
- Write a sine function whose graph is moved up one unit and left π units.
- Write a cosine function whose graph is three times as tall and twice as wide as the original cosine graph.
- Write a function that is reflected across the x-axis, moved 3 units down, stretched horizontally to be twice as wide, and shifted π units to the left.