Sinusoidal Transformations: Sine and Cosine

Topic:
Cosine, Sine
Drag the sliders to view transformations of sine and cosine functions.
  1. Briefly describe how the original sine graph changes when a = 2
  2. Click the Reset button and describe how the sine graph changes when b = 2
  3. What value of b will stretch the sine graph to be twice as wide as the original?
  4. Click the Reset button, uncheck the Sine box and check the Cosine box. What value of b will shorten
  5. What value of b will shorten the cosine graph to ¼ its original length?
  6. 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)?
  7. Click the Reset. Describe what happens to the graph when d = -2?
  8. Write a sine function whose graph is moved up one unit and left π units.
  9. Write a cosine function whose graph is three times as tall and twice as wide as the original cosine graph.
  10. 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.