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Trig radians

Learning objects Trig radians

TLF ID L7847

Use a unit circle tool to explore sine, cosine and tangent values in different quadrants. Determine the values for angles between 0 and 2π radians. Observe the symmetry and patterns of the functions to predict the behaviour of the graphs and the values for the functions in different quadrants. Observe the graphs animate and visually connect them with the unit circle tool and table values. Extend the functions beyond 2π radians. Find out how trigonometry relates to the real world. This learning object is a combination of three objects in the same series.

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Educational details

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

11; 12

TopicsCosine; Function graphs; Patterns; Sine; Symmetry; Tangent (Trigonometric ratios); Trigonometric ratios
Learning area
  • mathematics
Strand
  • Mathematics/Algebra
Student activity
  • Interactives;
  • Experiment;
  • Analysis;
  • Modelling;
  • Data manipulation and interpretation

Other details

Contributors
  • 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
Browsers
  • 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
Rights
  • © Education Services Australia Ltd, 2013, except where indicated under Acknowledgements.