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UCD Maths Support Centre

Graphs of Trigonometric Functions

These interactive GeoGebra worksheets allow you to investigate what happens to the graphs of sin cos and tan when you change the values of various parameters.

The graph of y=Asin(bθ+c)

In the first graph you can investigate what happens to the graph of y=Asin(bθ+c) as you change the values of A, b and c by moving the sliders. Note that if you want to return any of the graphs to their original state, simply click on the icon in the top right hand corner of the worksheet

You should note among other things that

  • As the absolute value of A increases, the graph oscillates more in the y-direction.
  • As the absolute value of b increases, the graph oscillates more rapidly.
  • A c changes, the graph moves along the x-axis.

The graph of y=Acos(bθ+c)

In the next graph you can investigate what happens to the graph of y=Acos(bθ+c) as you vary the values of A, b and c.

You should note similar effects to those that you found with the graph of y=Asin(bθ+c).

The graph of y=Atan(bθ+c)

In the final graph you can investigate what happens to the graph of y=Atan(bθ+c) as you change the values of A, b and c.

The effects here are again similar if we allow for the fact that the graph of y=tan(θ) is different in character to those of y=sin(θ) and y=cos(θ). In particular, note that as x gets close to odd multiples of π/2, the absolute value of tan(θ) gets very big.