Education Technology

Six Trig Investigation

Activity Overview

Students use interactive content to investigate the six trigonometric functions: sine, cosine, tangent, secant, cosecant, cotangent, including relationships between each. The unit circle animation helps build the relationships, which they derive and prove. The second stage of the investigation has students building relationships for double angle formulas, thanks to a series of visual prompts. The Word document can be edited to suit your needs, so too the companion TI-Nspire file. 


While the end result is for students to have a series of relationships for sine, cosine, tangent, secant, cosecant and cotangent, by building the relationships for themselves, students develop a great understanding of the ratios and relationships and the corresponding domain and range. Understanding trumps memory! The activity can be edited to suit the needs of each teacher. 


  • sine
  • cosine
  • tangent
  • secant
  • cosecant
  • cotangent
  • sin(2x)
  • cos(2x)

About the Lesson

Students can be given formulas to use blindly, however in this investigation, students are provided with an interactive version of the unit circle so they can display all six trigonometric ratios and therefore build their own formulas or relationships. Once students have finished building relationships, they can work on the double angle formulas. The companion word document (investigation) can be edited, so too the TI-Nspire file.