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# Trig degrees: tangent to 360

TLF ID L7846

Use a unit circle tool to explore tangent values in different quadrants. Determine the tan Ø values for angles between 0° and 360°. Observe the symmetry and patterns of the functions to predict the behaviour of tan Ø in different quadrants. Observe the graph animate and visually connect it with the unit circle tool and table values. Extend tan Ø for angles beyond 360°. Find out how trigonometry relates to the real world. This learning object is one in a series of nine 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.
• Students interpret a graph of tan Ø, from 0° to 360°.
• Students identify patterns and symmetry of the tangent function.
Educational value
• Enables students to compare and understand the key features of the tangent function (from 0° to 360°).
• Provides an interactive unit circle tool to ensure students work with general definitions of the tangent function, connected to the right-angled triangle definition.
• 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

10; 11; 12

Learning area
• mathematics
Strand
• Mathematics/Number and algebra
• Mathematics/Measurement and geometry
Student activity
• Interactives;
• Experiment;
• Analysis;
• Modelling;
• Multiple choice questions;
• Data manipulation and interpretation

#### Other details

Contributors
• Script writer
• Organisation: Erica Dale; Tungaroo Software
• Address: Manly NSW 2095 Australia
• Educational validator
• Organisation: Paul White
• Address: Strathfield NSW 2135 Australia
• Publisher
• Date of contribution: 20 Sep 2013
• Organisation: Education Services Australia
• Address: Melbourne VIC 3000 Australia
• URL: http://www.esa.edu.au/
• Subject matter expert
• Organisation: Will Morony
• Address: Adelaide SA 5000 Australia
• Technical implementer
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.