TLF ID L7850

Use a unit circle tool to explore cosine values in different quadrants. Determine the cos Ø values for angles between 0 and 2π radians. Observe the symmetry and patterns of the functions to predict the behaviour of cos Ø in different quadrants. Observe the graphs animate and visually connect them with the unit circle tool and table values. Extend cos 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 cosine function for angles expressed in radians.
• Students interpret a graph of cos Ø, from 0 to 2π radians.
• Students identify patterns and symmetry of the cosine function.
Educational value
• Enables students to compare and understand the key features of the cosine function (from 0 to 2π radians).
• Provides an interactive unit circle tool to ensure students work with general definitions of the cosine function, connected to the right-angled triangle definition.
• Includes challenges that highlight the symmetry and patterns of the cosine function.
• Contains associations with real-world periodic phenomena that are modelled with trigonometric functions.
Year level

11; 12

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
• 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.

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