Learning objects Trig radians: tangent

TLF ID L7851

Use a unit circle tool to explore tangent values in different quadrants. Determine the tan Ø values for angles between 0 and 2π radians. Observe the symmetry and patterns of the functions to predict the behaviour of tan Ø in different quadrants. Observe the graphs animate and visually connect them with the unit circle tool and table values. Extend tan Ø for angles beyond 2π radians. Find out how trigonometry relates to the real world. This learning object is one in a series of seven objects. Three objects in the series are also packaged as a combined learning object.

Educational details

Key learning objectives
  • Students apply the unit circle definitions of the tangent function for angles expressed in radians.
  • Students interpret a graph of tan Ø, from 0 to 2π radians.
  • Students identify patterns, symmetry and discontinuities in the tangent function.
Educational value
  • Enables students to compare and understand the key features of the tangent function (from 0 to 2π radians).
  • Provides an interactive unit circle tool to ensure students work with general definitions of the tangent function, connected to the right-angled triangle definition.
  • Represents the discontinuities in the graph of the tangent function,at π/2 and 3π/2 radians.
  • Includes challenges that highlight the symmetry and patterns of the tangent function.
  • Contains associations with real-world periodic phenomena that are modelled with trigonometric functions.
Year level

11; 12

Learning area
  • mathematics
  • Mathematics/Algebra
Student activity
  • Interactives;
  • Experiment;
  • Analysis;
  • Modelling;
  • Data manipulation and interpretation

Other details

  • Script writer
  • Name: Erica Dale
  • Organisation: Tungaroo Software
  • Address: Manly NSW 2095 Australia
  • Subject matter expert
  • Name: Ron Barassi
  • Address: Melbourne VIC 3000 Australia
  • Subject matter expert
  • Name: Will Morony
  • Address: Adelaide SA 5000 Australia
  • Educational validator
  • Name: Paul White
  • Address: Strathfield NSW 2135 Australia
  • Technical implementer
  • Publisher
  • Date of contribution: 20 Sep 2013
  • Organisation: Education Services Australia
  • Address: Melbourne VIC 3000 Australia
  • URL: http://www.esa.edu.au/
Access profile
  • Colour independence
  • Hearing independence
Learning resource type
  • Interactive Resource
  • Microsoft Internet Explorer - minimum version: 8.0 (MS-Windows) - maximum version: 9.0 (MS-Windows)
  • Firefox - minimum version: (MS-Windows)
  • Safari - minimum version: 5.1 (MacOS)
Operating systems
  • MacOS - minimum version: 10.6
  • MS-Windows - minimum version: XP - maximum version: 7
  • © Education Services Australia Ltd, 2013, except where indicated under Acknowledgements.