Transformations on Trigonometric Functions. Grade 11.

The interactive file below helps you to see what happens to the graph of the function y = cos x if we change the formula to y=a cos [ k (x-p) ]+v.

Originally a=1, k=1. p=0, v=0.

The black graph represents y = cos x. The red graph represents the transformed graph.

Change one parameter per time (drag the sliders) having other parameters the same as they were initially.

Observe how the changes that you make affect the graph.

Analize the TRANSFORMATIONS and RECORD:

CHECK:

• a- is a vertical stretch/compression, it affects an amplitude
• k- is a horizontal stretch/compression, it affects a period
• p- is a horizontal shift left or right, phase shift - the beginning of a the first cycle
• v-is a vertical shift up or down, it affects a baseline!

I hope it helps!