Trigonometric graphs

Sam Waterfield, narinder kumar, Sep 12, 2023

[b]A geometric derivation of the basic trigonometric graphs from the unit circle. [/b] The unit circle, simply put, is the most basic circle you can get: the circle centred at the origin with a radius of 1. This is a very simple but very powerful mathematical concept, particularly when building up a conceptual understanding of trigonometry. Explore each applet in turn to build up a natural picture of the basic trigonometric graphs (sine, cosine and tangent), before extending into a consideration of transformations. Questions follow each applet to structure your consideration of each graph alongside the unit circle.


  • 1. Trig ratios on the unit circle (SOHCAHTOA)
  • 2. Deriving the sine graph from the unit circle
  • 3. Deriving the cosine graph from the unit circle
  • 4. Deriving the tangent graph from the unit circle
  • 5. Transformations of trigonometric graphs

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Trig ratios on the unit circle (SOHCAHTOA)

[b]Important convention:[/b] Angles are always measured anticlockwise from the positive x-axis.[br][br]Use the checkboxes and drag the point P around the unit circle to show how the values of the trig functions change. Consider each function carefully in turn. Why is it useful to use the unit circle (radius 1)?
– Sam Waterfield

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