Education Technology

Six Trig Functions

Activity Overview

The six trigonometric functions: sine, cosine, tangent, secant, cosecant and cotangent are all inter-connected. In this activity students use a dynamic representation of the unit circle with each trigonometric function to identify relationships. They see why co-sine, co-tangent and co-secant are so named and where the identities come from, including the opportunity to build their own.


Students develop meaningful connections between the six trigonometric functions beyond the simplistic memorisation of ‘the third letter’ for cosec, sec and cot. Through understanding students are better equipped to answer questions beyond rote learning.


  • sine (sin)
  • cosine (cos)
  • tangent (tan)
  • secant (sec)
  • cosecant (cosec)
  • cotangent (cot)
  • Similar triangles
  • Pythagoras's theorem

About the Lesson

The six trigonometric functions sine, cosine, tangent, secant, cosecant and cotangent are represented on the unit circle. Students use these representations to build understanding of each function and to develop relationships between each by consideration of similar triangles and Pythagoras’s theorem.