Monday, July 20, 2009

trigonometry - six functions, unit circle


This sketch shows the six trigonometric functions (Sine, Cosine, Tangent, Cosecant, Secant and Cotangent) as distances on a unit circle diagram. The angle is defined by the positive x-axis and a point on the circle that can be moved manually or animated. The unit circle is depicted adjacent to a Cartesian coordinate system of the same scale, for an easy visual translation between two important representations of trigonometric functions. Individual functions can be hidden or shown separately.

Keywords: trigonometry, trig functions, sine, sin, cosine, cos, tangent, tan, cosecant, csc, secant, sec, cotangent, cot, geometric, radians, degrees, unit circle diagram, period, animation


  1. Hi Nate,
    I am very impressed with how non-clunky your GSP sketches are. Do you mind my asking how you do some of those things? First instance, how do attach your captions so they're just where you want them?

  2. Brian,
    The text can be merged to points by selecting both the text and the point and selecting "Merge Text to Point", which appears as an option in the Edit menu when you hold down the shift key.

  3. Very useful resources. Thank you.
    I also have a useful book related to this topic.

    Trigonometry For Dummies (2014).pdf - 7.2 MB

  4. Trigonometric ratios, fast app to find: sine, cosine, tangent, cotangent, secant and consecante of an angle